That's a bit overkill in terms of processing power, but it will definitely work! It's actually powerful enough to do machine vision and mapping!

One thing to remember is that the current draw for the Pi 3 will be much higher than the Pi Pico. Some students have had battery issues using motors + the Pi at the same time. They got the batteries in a sketchy industrial market here in VN though, so they were definitely not rated for very high current. This is one reason I use the Pi Pico and low power 6V motors -- it runs all day of a single very questionable lithium cell. Boots in milliseconds too, vs. much longer on Raspberry Pi + Debian, at the risk of comparing apples and oranges.

Another thing that was annoying, is to remember to put nonpolar capacitors across your motors if building your own motor controllers (most modules you buy will do this for you). Otherwise, noise from the e.g. brushed motors will probably make the Pi reboot constantly. I had this problem pretty bad -- it worked fine hand-soldered but when I got the boards from the factory it would fail often unless I put the caps in.

Anyway, if you're short on time and want to get the project done, there's also a thing called the Motorshield that will let you very quickly build a robot from the Pi you have. There are also LiDAR shields if you want to try mapping and fancy autonomous navigation. If you want cheap, you can't beat this motor controller module though (and you'll just need 1 for a differential-drive rover):

https://hshop.vn/products/mach-dieu-khien-dong-co-dc-l9110

You can generally find it anywhere in the world!