first of all: sorry for taking so long to answer this! a lot of things happened one after another and my brain wasn't in the best place for longposting — but also once i actually considered this question, the more i thought the more i had to keep thinking.
when KRITIQAL SUPER SONIC SHOWDOWN was happening (and if you're not familiar i really recommend checking out its tournament bracket and twitter poll thread, because there were some genuinely great outcomes and turns in that event) it suddenly became extra clear to me how appreciated every little background badnik becomes once they are given the spotlight, you just barely ever hear about people liking them beyond an occasional "remember this?" post.
so i don't even know if there are any characters that i personally think are underrated, because now i just have this deep conviction that every character has their fair numbers of dedicated sickos, so all of them are fine and strongly beloved lol.
what comes below is i guess just some of the less visible / discussed characters that i think are fun (as always i have trouble picking just one, sorry! hopefully at least one of these takes resonates with you):
Duke of Soleanna
one of the major story characters in 06 (and even some gameplay hints are suspiciously voiced by him from beyond the grave), yet there is very little ever said about the guy, if at all? Elise's dad who died some time after saving (and cursing) her in a lab accident, the end.
but i think it's very important to note how unhinged this man is:
overwhelmed by the grief of losing his wife, he starts a secret underwater lab project to resurrect a time deity from its living flame, hoping to reclaim control over his life and "rectify past mistakes". he even has the audacity to actually tell Elise that it's for the good of all humanity?? yes, Elise, everyone will be given a chance to live happily if we don't ever have to experience loss and pain and responsibility again, and yes, we will be able to bring your mother back! what a win-win scenario.
so yeah, i think the Solaris Project / Project Shadow parallels are cool, and love how 06 stitches its different stories together with loss and grief. my favourite part is that the root of the entire bad future apocalypse is literally a sad dad who would do anything except go to therapy, has the power and resources to go through with his plans, and fails, only making it 100 times worse for his daughter.
Professor Puccini
this one is less about a character and more about a situation, but speaking of research and accidents: there's a town mission in Shadow's episode that i think is nice. Shadow gets approached by a young man with an urgent request to save Professor Puccini: the man is speeding on a highway in his fancy red car, but there are monsters attacking him and lasers everywhere!! and if that's not enough incentive to save him, the professor is ALSO a core figure in local cultural research!! so please, Shadow, i beg of you, help grandfather the Professor....
and when you complete the mission and Puccini finally arrives in one piece, he thanks Shadow in a very sweet way, saying he's honoured to meet him, and i don't know. i just think this whole thing is a cute little mirror to that other time Shadow couldn't save anyone.
Lord Regis' Daughter, Sabrina
i hate her, i love her, she is my cursed pocket Nanami Kiryuu of the sonic series. when she went from dismissing and berating the Ultimate Lifeform, sending him on errands all over the town, to the tentative "thanks. so what's your name? no reason, just curious", i FELT her brain grow and rewire itself! best 5-minute character arc ever. Shadow's whole 06 episode and set of missions is a big fuck you to everyone disrespecting him, and Sabrina is the vessel for that. bless her and her awful attitude.
Middle-Aged Woman / Friendly Stew Lady
there's this woman in the castle town that worries about your well-being and invites you to come over after the whole Eggman situation is over, saying she will even make some delicious stew, For You. the game ending with the characters losing their memories of the story events just hits extra hard when you realise that it means neither of them will be able to come by for that stew anymore. T_T
Woman / Soleanna Castle Town Protector
another kind character in 06 is a woman who stands in one of the town's corners, watching the horizon. when talked to earlier in the story, she shares her concerns about Eggman, and says that she's keeping watch to evacuate the town as soon as possible if he strikes again — but when you talk to her later, she will ask if there's anything worrying you and say that there's no need to keep it all bottled up, offering to listen.
i even found this piece of fanart of her! please check it out because it's awesome.
[okay if i don't stop myself this whole post will be about 06 NPCs and town missions, both of which deserve their own dedicated posts because i'm not even scratching the surface here, so. finally moving on to other games.]
some GUN soldiers from ShTH 2005, like Bob Who Gets Repeatedly Got, or The Guy Looking For His Bike, are very funny to me.
(little did the latter know that it was Shadow who took it. and then crashed it. and then seemingly repaired it and gave it a cool custom paintjob? or maybe just grabbed another one. never hesitate to hurt a GUN soldier's feelings!)
overall these guys just have some really silly lines, like "men.... forgive me...." or "THIS is for my FRIENDS", i just can't not appreciate the delivery there.
the guy who loves the sea in Sonic Adventure is (sometimes) a vibe.
Do you like the view from the station?
I love the sea.
The sea's always there for me.
i also love the sea (and view from the station)! there isn't much else to add here because.. most of his lines are Just Like That, but it's so nice sometimes to feel understood by a random guy in a sonic game who is just standing there. unfortunately, he also hates sunsets and stars (unless they are shooting stars), and holds some other opinions which i can't quite relate to, so that's where my personal overlap with him ends, but the important thing here is knowing what you care about.
like the guy himself says:
Did you find what you're looking for?
I found myself!
By inquiring within.
President's Secretary
a rare case of recurring background character with a gameography of two (2!!) appearances, Secretary does all the hard work in the office while the President himself is only good for gushing about his beloved heroes Sonic and Shadow and looking at their photograph on his desk, with an occasional empty statement about whatever the current situation is. he's obviously not on top of his responsibilities, and poor Secretary who has to remind him of everything he needs to do just deserves so much better.. well, at least she has a cool SA2 menu theme of her own.
BONUS
this one is not exactly "underrated", but rather a character that is very popular yet the most common type of appreciation for them feels a bit too monotone to me personally:
E-123 Omega
not to rant a lot about it, but i really like that Omega's desire for destruction is directed at specifically Eggman and his empire, and his vengeance comes from personal bitterness first and foremost before he gets to know Rouge and Shadow and works with them more. this big guy (i always forget and then can't believe it when i remember that he is only 150 cm tall, with how tiny most other characters are in comparison) can fit so much drama!! and he cares about his team!! he tells Rouge about Shadow before going in to destroy the copies, and he was so conflicted over what he had to do in the future in 06! i wish humanity as a whole gave Omega's feelings more love and not just dry explosion arson comedy relief stuff (which is cool! just would be even better to have both more often, you know?)
BONUS 2
just got reminded of this one yesterday, and how could i forget!
she
Casino Bunnies from Heroes (and Maid Robots from Adventure) always deserve an extra shout-out for their hard work and served looks. just saying.
