2.5 is play after TVHM MS is completed. There is no PT3 or in other words a third MS play through.
Reason most people recommend that you stick to MS only missions is that once TVHM Warrior is completed the game sets quests rewards at Level.
Note they are not guaranteed to be level 50 if you accepted before TVHM mode before TVHM mode was finished.
Just because you finish TVHM mode than accept quests does not mean you will get highest or best weapon just a level 50 blue or higher. So farm the turn in a few tries to get see if you get better stats.
Note if you complete your TVHM mode than go back to PT1 do your "you will die seriously" re Terra than you will find he drops level 50 gear plus chests on way out will be set to level. This makes farming him easier for Level 50 gear.
People are split when to do green reward quests but almost all agree your blue/purple turns in are worth the wait to not accept unless TVHM mode is completed.
Note nothing guarantees you Legendary nor the best stats on items in game so again you may want to farm your turn in's on 2.5 re see what your getting-dash board re exit without saving than start game over to see if can get better stats on your rewards if you choose to do so.
Again to clarify there is no PT 3 re start new game with MS and new sidequests.
Also 2.5 mode does not guarantee all vending machines will be set at level 50. Some of the DLC ones are set to only 48 to 49 for sure.
Hope this helps on any decisions you need to make.
Personally if you are going to for all achievements do one character and do everything on PT1 than start your TVHM mode. This way you can than save all your PT2 quests until 2.5 mode than hopefully get best rewards.