Reference request for Effective field theories

Situation

I’ve taken a course on QFT, covering canonical quantization (of the scalar, EM and Spinor fields), Feynman diagrams and rules, etc. — it was your basic one-semester introduction to QFT.
I’ve also had an introduction to the Path integral formulation and was shown how to do basic calculations in it, but I didn’t have as much practice in this area as I would wish…

Reference request

I’d like to learn more about Effective field theories (EFT) and of course I’ve noticed that there is a lot out there covering this topic. Unfortunately, this makes it quite hard to pick a specific resource and follow it.. I’ve come across a lot of review articles on arxiv (for example [1] and [2]) but there also seem to be some books on the topic (like [3] and [4]). The issue is that I don’t know what to pick for my needs. I’d like to read something that gives me a reasonable introduction to the necessary background (i.e. the Path integral formulation seems to be quite important, so it would be nice to have a chapter or so focusing on what properties are relevant, etc.) but even more importantly, I’d like a resource that is as rigorous as possible on the mathematics side.