It's semantics. It's minimizing. It's an excuse.
The variations are seemingly endless. An EA isn't cheating because it didn't turn physical. Sexting isn't cheating because the other person isn't physically present. Kissing isn't cheating because it wasn't sex. Sexual gratification short of intercourse isn't cheating because it wasn't intercourse. Intercourse isn't cheating because "it was just sex", didn't mean anything and wasn't emotional. Blah, blah, blah.
Based on what you wrote, it appears that your husband had multiple EAs and sexting/social media interchanges. That's cheating and it is many times, so that makes him a serial cheater. Even if you accept the terms "inappropriate behavior" and "boundary issues", it still points to the same thing -- that he has a character gap which he repeatedly is trying to fill/numb by pursuing other women.
he gets it now, and I don't need to worry that he'll engage in these behaviors again.
And here is the classic line from a serial cheater -- the promise that everything is under control and that it won't happen again. Until it happens again.
Thoughts, fellow SI friends?
Given that you still are receiving TT, you are continuing to receive additional Ddays. The potential to R depends on the ability to rebuild trust and additional TT only makes R less probable. Your WH needs to know that he needs to come fully clean otherwise any chance to rebuild the marriage is going to be lost.
In addition, your WH's path to becoming a safe partner needs to include...
1. Seeing himself as broken and needing help
2. Digging deeply into himself to find the character gap at the root of his brokenness.
3. Finding his "Why?", taking responsibility and doing a ton of hard work to make a substantive change inside of himself.
Minimizing everything by calling it "inappropriate behavior" and trying to avoid doing any real work by promising that it won't happen again is an indication that he isn't doing any of the above. Unless that changes, he isn't a safe partner and the odds of a future affair (either emotional or physical) remains high.