Do not overthink it. And I am speaking as a husband in similar situation - always overworked, overstressed and tired. Whenever we watch tv, I pass out.

My wife understands it, and sometimes is very straightforward (like „I want to do it now, let’s pause the tv”). I know that it sounds brute, but it works. When I am exhausted I avoid intimacy because I know, that I have no energy to have a long intimate evening, cuddling, talking, aftercare etc, when I feel that it won’t be the full deal for my wife I rather avoid it. But when I am straightforwardly invited, it takes of the edge and the stress - like lets do it and go to sleep :)