Plug-in vanity lighting

Almost every bathroom has one vanity light, mounted above the mirror, because that is where the builder put the junction box. It is also the worst possible position for the job.

Light from above lands on your forehead, nose and brow, and leaves shadows in your eye sockets, under your nose and beneath your chin - exactly the areas you are trying to see when shaving or applying makeup. Brighter overhead light makes those shadows darker, not lighter.

The fix is light from the sides, at roughly eye level, from both directions so each side fills the other's shadow. And the good news for anyone renting is that none of it requires touching the fixture above the mirror. That stays; you add to it.

KGC milky glass G25 - the bulb for whatever you add. CRI 90+ at 2700K behind diffusing milky glass, dimmable. At a mirror, color rendering and diffusion are the two things that matter, and this does both - the milky glass stops a bright point being reflected straight back at you.
Cons: no lumen figure published, only a 40W equivalence, so count bulbs generously.

NIORSUN rechargeable sconces - the cordless side lights. 300 published lumens each, a 3000K setting, and no cord - which in a bathroom is a genuine safety advantage, not only a tidiness one. A pair either side of the mirror is the whole side-lighting fix with nothing near the sink.
Cons: 300 lm each is moderate; they need charging; and not every battery sconce is suited to a humid room, so check the maker's guidance.

Sunco clear G25 - for the existing bar. 500 published lumens at 2700K and CRI 90. The first and cheapest move is simply putting better bulbs into the vanity bar you already have.
Cons: clear glass glares if the bar faces you; frosted is usually kinder at a mirror.

Lutron Credenza plug-in dimmer - for plug-in sconces. Dims a corded sconce with no wall work, so bright morning light and a soft evening level come from the same fixtures.
Cons: it sits at the outlet - and in a bathroom, the outlet position determines whether a plug-in route is safe at all.

A bathroom is the one room where a plug-in route needs genuine thought, because electricity and water share the space.

Keep corded fixtures away from water. No cord should run near the sink, bath or shower, and no plug-in fixture should be mounted where it can be splashed. If the only route for a cord passes the basin, that is the case for a rechargeable sconce.

Use GFCI-protected outlets. Bathroom outlets are required to be GFCI protected, which is what cuts power if a fault occurs near water. Plug only into those, never into an extension run in from another room.

Mind the location rating. A bathroom is a damp location by definition, and a sealed fitting is also an enclosed one. Both specifications, and the difference between them, are in wet rated vs damp rated.

Mount at eye level, either side. Two sources flanking the mirror, roughly at the height of your eyes, cancel each other's shadows. One on a single side just moves the shadow across your face. The room plan is in bathroom lighting.