Thinking about Wolfenstein TNO, I think the keys to why the stealth and shooting felt so naturally intertwined were:
1.) Have a bit of a grace period if the player gets spotted. Many times in TNO I accidentally left cover right in the sight of a a nazi, had them say "what is that?" and then I backed up back into cover and they just resumed their patrol.
2.) If the player has to fight after getting spotted and triggering the enemy alert mode, make the player really strong.
3.) Have some sort of "alert mode off button". Usually in TNO, this means killing the nazi commander broadcasting the alarm. It instantly ends the alert mode, and as long as you kill all the nazis left afterward, you're back to sneaking. Bonus point is, if you sneak around and stealthily kill the nazi commander first, you're then free to deal with the others in the area however you want. Take them out quietly or loudly.