It looks like it could use a bigger pot, yes. figure canopy size is correlated to the amount of root growth below ground. So, it should be well-rooted.
if the current pot slowed it down at all, it may take a few days before you notice significant growth after transplant, but it'll kick back into gear.
even if your pot doesn't have a zipper, you won't shock a plant from potting up unless you pull out the trademarked GI Joe Kung Fu grip and destroy the rootball with some retard strength as you do it. I'm not making fun of you. I'm pointing out the lengths you'd have to go to to shock a plant while potting up. Also, moisture definitely helps hold things together, but at this point the roots will do the heavy lifting in this respect... for a much smaller seedling on first transplant, the moisture is even more important to hold rootball together.
with fabric, sometimes a bit of roots grow into the fabric. that won't cause much stress to worry about. can push a trowel down the side to make it slip out easier if you ever get pots without zipper or velcro etc. by this point, the roots and plant are pretty sturdy. Loosen up the fabric around outside and simply pull it out... can fold fabric pots down on side, too. with hard plastic pots i just warp the outside a bit to seperate it from the medium.. slides out easily, too.
I have yet to see a plant of mine get 'shocked' by potting up. hundreds.. several hundreds. the risk is so low with basic competency that it is just an urban myth. Transplant shock is more about outdoor transplants where you do cause severe and significant damage to roots, because you are cutting off significant portions of the root mass, which you can easily avoid with a potted plant, obviously.
definitely plan to do potting up in vege to be extra safe. crazy contexts do happen but usually can avoid them with a bit of planning. in the end, you do what you have to do even if self-inflicted, lol. a pot up in flower really shouldn't be a problem either, but easily avoidable too.