How do you play such a board?

Forgive me, I cannot remember the exact hands but I flopped a J high flush on a one tone board, no pairs. I was OOP. Preflop I did a raise from small blind and was called by the big blind.

I check-called flop and turn. (About half pot bets). River was a pair board. I check opponent bets close to pot on river, I folded.

It feels like a bluff, because there isn't many hands that take that line (An ace high flush would have bet twice, but another pot sized bet on the river on a pair board?) (Is he telling me he bets twice (flop and turn) on sets on a single tone board? Which is possible though) Also a queen/king high flush wouldn't value bet so thin on such a scary board. Either he has the house or is bluffing, but I am only beating a bluff here, so I folded.

I check-called instead of check-raising as check-raising is too stong and seems like only the ace and maybe king high flushes would continue. (Which I would lose to). Donk betting all three streets also doesn't seem all that profitable, but is a possible scenario. Maybe smaller flushes might call if they put you on a bluff. Donk betting two streets might be good, but if he raises on the flop or turn, can you continue?

Anyone has a standard way to play these kind of scenarios?

My reasoning for checking on the flop was to let him bluff and to check call.
Turn I considered leading out to protect against sets and 2 pairs (But then again I was OOP, so I check and was planning to value bet small-med on the river if he checks on turn). But he bet again on the turn, I have to call with a made hand and evaluate again on the river. River was a pair board (He bets 3/4 size bet). I folded as he possibly has a set that became a fullhouse. Either that or he made a very good bluff. Flushes won't play like that in my opinion (Probably checking river already).

It seems mid-high flushes on this single tone boards are very frustrating (Especially OOP). Where you can't simply xr for fear of meeting the nuts. but checking or betting out is still very vulnerable. What to do when board pairs? or if he re-raised on flop do you go all-in with J high flush? Etc...

By the way, I feel the answer to my question is that it is very situational to opponent's tendencies and stack sizes. But if anyone has a "standard" way that they will play this hand, feel free to post.

No way

i would cbet most of the time and sometimes check to opp which like to stab IP

I would cbet half pot with entire range, bet bigger on turn like 2/3, and then check if called twice, and eval river