I’m partial to using Ubiquity UniFi lately. I’ve heard people use “Ubiquiti UniFi LTE Backup Pro” to do this (Designed specifically as a failover device: plugs into UniFi gateways, Uses primary ISP always, LTE only when wired WAN fails Clean integration for UniFi users) So that is fairly likely what I would probably look into doing if I were to do it myself since I already have a UniFi dream machine.
I’ve heard people use Peplink Balance 20X (or B One Plus) (Popular small-business router with a primary WAN port and optional LTE SIM slot (you’d have to get your own SIM mobile data account). Strong failover logic — you can prioritize WAN first and LTE only on outage)
GL.iNet Spitz AX (GL-X3000) or Spitz Plus (GL-X2000) - these run on OpenWRT as their foundation so they’re very customizable. You can set them up to normally use your ISP via WAN port. Then have LTE kick in only when WAN fails.
Netgear LM1200 (LTE Modem) + another Router that supports failover - Not a router itself, but acts as an LTE modem on standby. Connect it to the secondary WAN port of a router that supports failover (e.g., Asus RT-AX series, TP-Link Omada, or Ubiquiti UniFi Dream Machine). Your router decides when to switch from ISP → LTE. - similar to this, there are a whole bunch of other LTE type options. I remember when I was looking into them a few years ago there were a bunch that even had free data up to so many hundreds of megabytes or gigabytes per month for free, so if you never used it you never got charged, but if your main internet is unreliable, you might want to have a router that allows you to use settings to restrict which devices can actually use it when it switches to LTE So your other devices don’t cause you a lot of overage charges during an outage like 4K HD media streaming services.
Since you already have the Wyze mesh routers, and may want to continue using those instead of wasting money on an entirely mesh system, the simplest DIY path is:
Get a small router with WAN + LTE failover (GL.iNet or Peplink).
Put it in front of the Wyze Mesh (as the main router).
Wyze Mesh then just acts like normal Wi-Fi nodes, blissfully unaware… May want to put them in bridge mode so there is no “double NAT conflict.”
But if you use any of the above solutions, you can have any alarm system you want And they will all have cellular backup even if you ever switch to a company that doesn’t offer or provide it, including the Wyze HMS. It will also probably be cheaper than paying an alarm company for cellular backup (note When you set up an LTE account for mobile data backup, if it’s only going to be rarely used when your main internet goes out, you probably don’t need an unlimited internet plan or something really expensive).
Hope that helps to at least give you a starting point of things to look into.

