There are all sorts of apps for smartphones that record your track (position and time).

You don't need sensors to use a Garmin or a smartphone.

I have no idea of your budget.

You might consider buying an inexpensive mount and seeing how well your smartphone would work.

Maps.me is a free app that uses downloaded maps and can generate routes (without needing cell access). You can load tracks (courses) to it but it can't use them to announce turns. Maps.me doesn't record tracks in a way you can export them to other apps/programs).

The big advantage of the cycling Garmins is that they can provide turn guidance for a track you copy/load onto the unit.

Even if you have a Garmin, maps on a smartphone is likely going to be useful (the screens on the Garmin's are rather small).

No reason a phone can't work. You just need a good mount, some sort of water resistance, and an external battery.