I like barrelling to fold out equity and take it down. xc turn is an option as well.

around ~2/3 is catching everything sizing's( fold equity, growing pot, getting value...)
This hand is bit thin to bet turn vs 20/13 guy. If called turn we are snap checking all rivers except T and 9 and looking to x/fold.

I think the idea is fine but the sizing is a bit too large not needed for it

Imho when bet 0.9psb you're isolating yourself with the strong part of the range of btn, and T9s is too weak for value bet and i think one consequently of betting wide merged range is also that our checking range is too weak on river.
Check seem a good action .
If turn is unopened, river on blank we can bet for take value from middle/low value of his range, from hands like 99-77/7x ; or c/c for take value from some bluff like 98/QJs/KJs/44

Like the play - the flop is good for you because its a very dry board and you still have all the value hands in your range - like the turn barrel again because you get him to fold out a lot of middling pocket pairs that defended flop