QI bloomed a Debut holomem [Houshou Marine] on my stage to hBP02-032[Houshou Marine]. At this point, I did not use the bloom effect "Houshou's Pirate Crew". After that, I used hBP06-090[Bloom Stage] during the same turn, and bloomed my hBP02-032[Houshou Marine] to another hBP02-032[Houshou Marine]. During this second bloom, can I use the bloom effect "Houshou's Pirate Crew"?

ANo, you cannot.
A bloom effect's activation is mandatory, so it was regarded that you have already used the bloom effect [Houshou's Pirate Crew] during the first bloom.
As such, "you may only use bloom effect "Houshou's Pirate Crew" once per turn" will take effect, and bloom effect [Houshou's Pirate Crew] cannot be used in the same turn.

QIs "You may only use Bloom Effect "Houshou's Pirate Crew" once per turn." for the 《Bloom Effect》 "Houshou's Pirate Crew" of hBP02-032〈Houshou Marine〉 different from [1/Turn]?

AFor [1/Turn], each of those abilities may only be used once per turn. However, for the 《Bloom Effect》 "Houshou's Pirate Crew", it means that 《Bloom Effect》 of the same name may only be used once per turn.
For example, if a hBP02-032〈Houshou Marine〉 that has already used 《Bloom Effect》 "Houshou's Pirate Crew" is on the stage, even if another hBP02-032〈Houshou Marine〉 was bloomed, the 《Bloom Effect》 "Houshou's Pirate Crew" will not trigger.