I have a second SIM card for my phone number (for a tiny fee) ... I need to direct where SMS go, but it rings on both.

You could probably also setup call forwarding from your work phone to your personal dumb phone - there will likely be an extra per-call cost.

HMD has released in India a semi-intelligent phone, the HMD Touch 4G, for (the equivalent to) 40€.

Can you talk with the IT team?
I was able to switch my MFA to a Yubikey.
They rolled out the MFA policy quite recently and I immediately sent an email like "Hello. I do not have a smartphone. What are my options?"
They also had the option for SMS verification, but I had been looking at getting a Yubikey for myself anyway so might as well get work to pay for it.

If you tell me what you want to achieve, I might be able to help you.

Put the sim in a dumbphone and share internet to smartphone over wifi or bluetooth when needed

do you call much. tracfone its easy to pick up cards or up your minutes online. their unlimited is fine to but honestly I find the minutes more useful as I don't even like being on the phone.