Airport express isn’t designed to be used as primary router.
Size isn't everything but the Airport Express has two slow (by today's standard) 100mbps ethernet ports and N wireless.
The last of the Extreme Apple made.. which is slow cf modern routers, has a much faster 1Ghz processor, 4 gigabit ports and AC wireless. It is clear and obvious as a router the Express is TOY Fisher Price version.
what is the difference/purpose of Airport Express vs Mesh Routers?
Airport Express uses the old fashioned wireless extend. It will help fill in a dark area with wifi if all the conditions are just right. It was designed in 2011 (Assuming you have the latest Gen2) well before mesh came on the scene. At substantial speed cost.. half your expected speed.
Mesh routers are much later and improved design cf the above.. much more powerful processors, AC or even AX wireless and far less limitations. Mesh creates the best connectivity setup itself. Express is limited to a single Extend from one main unit only. Mesh is self discovery fastest route through several units if needed. There is a speed cost but the better tri-band versions will still sustain Internet speeds across your whole house.
Mesh is designed for the much faster Internet connections of 2020's .. Express was designed for <100Mbps cable or even ADSL connection.
But the Express has a major feature nothing else has.. airplay. A built in audio out is unique amongst routers.
I am in the process of getting Apple TV and want to update routers at same time.
ATV in some ways takes over the role of the Express airplay.. since Apple ceased production of all Airports nearly 3 years ago now.
You definitely want to buy modern mesh system .. but you can keep your Express if you have older audio equipment without built in airplay. It will work fine as a client on the mesh system by wifi or even better Ethernet.
Or sell the Express.. the Gen 2 get fantastic prices on eBay.
For the best mesh system to buy.. read the reviews and check your budget, how big your house is and what speed you want in the dark corners.
https://dongknows.com/best-wi-fi-6-mesh-systems/
https://dongknows.com/best-wi-fi-5-mesh-systems/