That works to minimize your smartphone use, but you may be encouraging people to use SMS instead if that allows them to get ahold of you sooner or for emergencies. I am a bit confused by what a “work phone” is. Until now I assumed it was strictly for business, but banking and government apps are quite personal.
Is this work phone under a personal phone plan tied to you or heavily associated with your name? If so, I’m not sure if there’s much use for carrying around a feature phone. You could have one to sign up for services if it serves as a somewhat anonymous phone (both the device and phone plan must be purchased in cash and you cannot give up any personally identifying information for this to be the case) but if your “work phone” (which just sounds like a general use phone?) has a number tied to it, you may as well just stick to that so you can use Signal wherever possible.
VoIP providers like JMP Chat or MySudo would allow you to have multiple numbers on one device in case you need separate identities, but if everyone knows you by the same name and adds you to their contacts under that name, there’s little benefit in doing that.
A more advanced all-in-one solution could be to anonymously purchase a GrapheneOS phone and pre-paid data plan, never use its true number, and only stick to VoIP numbers for proper separation. You’ll probably still need a backup genuine phone number for services which require it, so a feature phone could still be useful. If your finance apps prohibit use on GrapheneOS and you tested that they don’t work well in a mobile web browser, instead of a feature phone your “backup” phone could just be a cheap smartphone. (A new low-end Samsung Galaxy gets you the best value as it’ll receive security updates for much longer than other budget smartphones.)
Sorry if I got too much into the weeds but I’m really confused by what you’re trying to separate and how you plan to do it. Achieving strong separation by using multiple devices costs time, energy, and money. I only go into detail because doing it sloppily probably isn’t worth doing at all.