Your question made me curious, so I contacted a large cricket sticker manufacturer (Stickmore Design & Printing, an Australian company; probably named after the founder, Mr. Stickmore, since surely, no company would base their name on such a groaner pun). I asked about the type of glue they use, and what they considered the useful life in normal use. This was the reply (I'll exclude the contact information since this is a public forum):
Thank you for your message.
All our stickers are digitally printed and created using self-adhesive polymeric vinyl. We use two types: white high tack and clear pressure-sensitive vinyls; depending on the job. The printing machine uses eco solvent inks and we finish the job with an overlaminate for additional protection which includes UV protection. The stickers are also contour cut by us into any shape.
In terms of life, this is always difficult to predict and I don’t know anyone that would like to put a number on it but, hopefully, I can give you some idea that might help. We have been supplying stickers to bat makers since 2017 and the feedback is that the stickers should last the useful life of a bat. Having said that, the bat must be cared for and a bat cover is highly recommended to prevent the stickers from being scratched by rubbing against items in a cricket bag e.g. spikes and zips. I, myself, use a bat for a couple of years before doing a full refurbishment and this includes a change of stickers (only because I can 😊). I also know of a senior male cricketer who is using the same bat for 4 years with the same stickers.
I hope this response is helpful but please let me know if you have any further questions.
It sounds like they don't know what type of glue it is. They buy two types of self-adhesive vinyl stock from a supplier, "white high tack" and "clear pressure-sensitive" (I'm guessing less-than-high tack). Whatever the adhesive is, it works for them, so it doesn't matter, and they don't care about the details.
You could find suppliers of self-adhesive vinyl stock and ask them, but you wouldn't know if their product is what's used for cricket bat stickers. Even if you ask about vinyl suitable for cricket bat stickers, you won't know if it's the same glue or how good it is.
Whatever it is, it's applied at the vinyl factory, probably with a process you couldn't, or wouldn't want to, duplicate at home. The glue is also probably an industrial product sold in large drums for a manufacturing setting. The same glue may not be available in a small retail package.
So this doesn't answer your question, but at least it prunes the tree you would need to explore. There are glues that will stick vinyl to wood that you could apply, but you would need to start with non-adhesive vinyl. If you apply your glue over pre-applied glue, the sticker is still held on by the lousy glue.