CliffordK

First of all, verify whether the 7-speed bike is using a cassette or a freewheel. Both are available.

https://www.sheldonbrown.com/free-k7.html

You can purchase 8/9/10 speed freewheels, but I'd avoid going down that route if possible.

If you have a cassette, as far as I can tell, Shimano is the only company that still makes a 7-speed freehub (the splined part the cassette sits on). So, if you have any hub that is not a Shimano hub THAT USES A CASSETTE, then it is likely an 8-speed hub with a spacer behind it.

For MTBs (as well as large cassette road bikes), the 8/9/10 freehub will also fit a 11 speed cassette.

You'll likely end up with a pile of upgrades to do though.

1. New Cassette
2. New shifters
3. If integrated shifter/brake levers, then the whole things get upgraded.
4. New Rear Derailleur
5. Possibly a New Front Derailleur.
6. New Chain.
7. Rear wheel upgrade or perhaps both wheel upgrade?
8. Crankset???? See below

That gets you down to the crankset. In general, your 10 speed, and perhaps 11 speed chain will fit onto the older chainrings. But, it may not be fully compatible. You'll run a greater risk of dropping the chain between rings. At least on road bikes with 11 speed, there is also a chance of rubbing when cross-chaining using old chainrings.

The other thing that has happened is that many older bikes had triple front cranksets, while newer MTBs are moving away from that. Many are even moving to 1x cranksets, and multi-gear on the rear. At least on road bikes, few modern shifters support a triple on the front, and derailleurs are becoming less common.

I tossed in wheels that could also be upgraded, if you want something different.

Kind of munching words there a bit. Skewers always CLAMP DOWN.
If it is "bolt down", that would be a bolt down axle.
A new "twist type" might be a "thru Axle". That certainly would be a distinction to look at, especially on the more expensive bikes. For a "commuter bike", it won't make a lot of difference.