What are some ways to make a tiny bathroom have more space/storage?

vertical storage....they make storage units to put behind a toilet

Put a shelf above the door and along any walls at the same height to store extras. Use baskets to contain small items. You can put extra towels-just fold or roll them the width of the shelf, toilet paper, etc. on these. Use pencil cups to hold makeup brushes, mascaras, & eye pencils. I have a clear glass cake plate to hold my toothbrush holder, small box of tissues, and a jar that has q-tips. The cake holder gets these items up off the counter top and looks pretty. If you have space, use a small plastic 3 drawer storage unit to hold makeup items and then the top of that can hold tissues, etc. If you have wall space next to your vanity, install narrow shelves to hold makeup jars.

go vertical. nobody really likes the over the commode shelves, but they can function well. i have baskets on that type of shelving for grooming tools, extra bars of soap, lotions, towels go on a wall mounted "coat rack" pine board with tri lobed hooks.

Shelves. I use a set over the toilet and another to the side of my sink. I have farmhouse design so Mason jars hold my makeup, brushes, etc.

Look for room behind the bathroom wall to put narrow shelves or a bookcase. You could also put one of those over the door shoe holders with the pockets to hold make up, and all those little things that like to hang out on the counter all the time, it probably could hold some cleaning supplies too. On the side of the vanity or a shelf, you could put in some cup holders to hang curling irons, blow dryers, straighteners, etc., or get large S hooks and hang them from a towel holder on the ends.