Since you mentioned anonymity in the post title, the easiest answer to give is "almost impossible". Anonymity in simple terms means not to be identifiable, but with the mobile network being an inherent tracking network and makes it easy to triangulate you, forget about anonymity. Not to mention many governments demand KYC for a SIM Card.
You could, with a lot of effort, costs and incredibly careful opsec figure out a solution. My best bet would be a GL.iNet MUDI V2 router with blue-merle and constantly swapping SIM Cards and IMEI numbers (at the same time) to make it harder to identify you. That's illegal in many countries though, plus one little dent in your habits (e.g. having your router turned on at home or within a radius or in spaces with cameras) and you're identifiable. It's very inconvenient and likely not necessary for your threat model. If it was, you'd probably worded this differently and made some research to ask detailed questions.
But to the good news: You might instead look for privacy aka control of which data you share with whom. A router with Mullvad, many open source apps and especially GrapheneOS can give you that. Check out privacyguides.org for more details and recommendations.
When I was using only one GOS phone, I did regularly bring a MUDI V2 with a SIM card so I could operate my GOS phone entirely in airplane mode and only use mobile internet where necessary. It didn't give me anonymity but a bit more privacy and control.
Nowadays I have two GOS phones. The private one is still locked down, multiple users, airplane only, no google services etc., but the business/work phone needs a SIM card and Google services, so it became my hotspot router for the private phone (both run their own VPN apps because there's no Hotspot over VPN functionality). It's a faster hotspot anyway and so much more than that. This is specific to my situation though and might not fit your needs.
I recommend you do some threat modeling and make sure to solve the important issues for yourself first. Mobile network is more of an endgame arena, you'll be more effective elsewhere. For most people, a simple GOS installation with Sandboxed Google Play Store and a SIM card installed is more than enough and honestly it would be for me too if I wasn't so much into making my life unnecessarily hard. GOS with default settings puts you back in the driver seat and from there it's only diminishing returns you might not even need.
But to answer your question: Yes a Gl.iNet router with Mullvad is neat and has its purpose. Don't let me ruin the fun for you, just make sure to properly manage your expectations, because it won't give you anonymity.