It is surprising there isn't a smart way to do this easily.
You can imagine using toy cars and such but achieving the constant very slow movement is critical - and difficult.
You can rotate the camera on a clockwork egg timer for not much money and the effect is quite good.
If you are looking for budget time lapse movement you can use a motorised telescope mount. I got a second hand one for about £200 and it allows very accurate/repeatable vertical and horizontal panning. Here's an example of it in use at about 20s.
Edelkrone does some very clever stuff.
Their slider have a folding system and they take little space when you carry them, but still allow for a good range of sliding.
For timelapse of course you need it to be motorized, while for regular video it is possible to use a manual one https://edelkrone.eu/products/sliderone-pro
Funny this pops up, yet again (last night and the night before) I have been looking at sliders. The price of motorised is way out of my league at the moment for what I'd use it, so looking for cheap manual operated ones.
A bit late now if you've already bought the slider, but you could consider shooting a wider angle and then panning and zooming in software. If you shoot high res. pictures for a timelapse or video in 4k, downsizing to 1080p gives you quite a lot of leeway to zoom and pan without any further loss of resolution. Resolve does a very good job of this and is free.
Ive been using the Digi slider autopan this is the first effort.
There were a couple of jumps on the last section where i had the belt too slack since tightening its been as good as gold.
I think long term i will probably go for the syrp system as its modular and does pretty much everything.
For editing I've been using LR time-lapse and lightroom, then bunging it into FCPX.
Surprisingly it's actually pretty good. I'm using a heavy setup on it -- need to test if it's over the recommended amount, but I don't think it is. At the ends of the slider there is some flex but really not much at all. Using the Pro X Long. Pretty strong!