Hi OP. @leonardo871 - I was a very very anxious person in relationships for about a decade - until I had therapy so I have a lot of things I can relate to here and I can tell you what worked for me. (I am now happily married!)
Firstly - you are wise to have recognised your anxious attachment style - the problem with this is it makes it hard for you to see the wood for the trees/ to recognise when someone is untrustworthy/ simply a poor match for you or if you are anxiously expecting to be let down because of your own lack of self worth.
I'm sure you have heard of the term hyper vigilance. you are hyper vigilant to threat - to the idea that someone will let you down/ be unreliable/ hurt you - while other people may be aware of that risk they will more calmly just think - oh well if this guy turns out to be a dick Ill end it.
One of the thought patterns I became aware of was that instead of thinking that I was panicking that I would be mistreated.
Yes this guy may not be right for you - you can only discover that with time! He genuninely may be someone who doesn't text much - how is he in person? Has he spoken to you about how he feels about you/ what he thinks about the relationship at all?
You have to be realistic about your needs. While you can deal with the over anxious mind you are also going to need someone committed open and kind. Some women might not mind a flirty/ flakey partner if they are good in other ways - but that wouldn't have worked for me and it won't work for you.
Decide what your boundaries are - talk them through with your therapist !
Accept that it may take a few more weeks to work out if this guy is committed and kind enough to be with - I don't personally think texting is the sign of that but it may mean you are not matching in temperamant.
Set yourself a month of noting how his behaviour makes you feel and talk through with therapist - if he is kind and caring in person and you feel you know where you stand - maybe the texting doesn't matter. My husband isn't a big text/ whatsapp communicator but I am - doesn't mean we are not well suited.
However if this guy makes you feel crap and worried a lot of the time - you may need to have an open conversation and say you personally need a bit more commitment. If he is the right guy he will be okay with that.