look at ebay/amazon for loo lights.
night sensor ligts - there are all sorts, word soup will find them.
This sort of thing uses AAA x 3, butthey can be recharegeable of course. I have one poked in my bedside table cubbyhole
Illuminate your bathroom in a creative modern way with our Toilet Night Light! This smart toilet light is flexible, you can easily bend it for any toilet seat or install it anywhere that glows in the dark.
www.ebay.co.uk
There are two types of led with those - make sure the one you get includes White as a colour. YOu can select the colour with the button on the thing.
Not bright - depends how much light you need. You can see what's where but couldn't read with one.
MY bedside one lasts months.
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These are much much brighter, more like a torch. You can easily take out the silly pattern screen in front of the white led. Theres'a coloured LED as well which is pretty pointless. It has a 500mAh recharcheablebatt , soldered/welded in, which I imagine is bloody awful quality and won't perform well over time, but better for your purpose.
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I did have a thing like this :
https://www.ebay.co.uk/itm/286905121301
which was OK but died when the rechargeable batt gave up. It started needing to be charged about every 3 weeks, after 6 months of covering a landing. Pathetic llittle battery probably 110mAh., aboout 2cm sq x 3mm thick.
You can of course buy much better rechargeable thin 3.2 or whatever volt batts for a few quid. Like the old phone batteries.
