Bottom bracket has play. Can I still tighten this, or do I have to replace it/fix it properly? Tools? (incl. videos and photos)

Question

I'm staying with a relative and borrowed her bike for a ride. It now has play on the bottom bracket - as shown in videos below.

TL;DR

Is it possible to judge if I can still just tighten this, or do I have to replace it/fix it properly?

And what spanner/wrench (or other tools) do I need for the non drive side?

The relative doesn't have many tools or a calliper gauge, so I'm hoping someone can assess what I need to buy and do from the videos and photos.

My observations so far

I'm fairly sure it's an adjustable BB.

Drive side

The drive side looks very much like a fixed cup with two wrench flats spaced at 36mm, as shown here

Non drive side

I couldn’t find an example of the non-drive side online. On first impression, the outside of the bearing setup itself looks similar to the setup in Park Tool’s article and video about One Piece Cranks (I know the relative's bike has a square taper BB, I really mean just the cup/nut situation looks similar).

But I think there are just two parts visible: a fairly usual lockring, and a seemingly unusual adjustable cup adjusted with a simple hex spanner/wrench (as opposed to separate locknut, keyed washer and a notched cup).

In other words, I seem to see a thin nut with a large flange, and I can only suspect that there’s a cup on the inside of that flange. I certainly cannot see any notches in the flange, so I am fairly sure that the flanged nut is actually the outside of the adjustable cup.

(edit: I did find a video with a setup just like mine, best view starts at 5:48)

I have no way of telling if the bearings are loose or caged - and I guess it's impossible to judge. It's a cheap 28" bike, probably from around the year 2000.

Finally, for context, the relative only uses the bike for gentle rides like to the shops. Unfortunately I rode it some 40 km and pushed much harder than the relative does.

Proper questions

I am keen to ask some specific questions to recap, but I know they might be the wrong questions in my situation:-)

1. Can I still just tighten this? Or is it so far gone that there’s no chance and I have to replace it/fix it properly?
2. Is it possible to judge with any confidence the size of that hex nut, which I suspect to be the end of the adjustable cup?
3. Will I be able to tighten this with a thin flat spanner (wrench), without removing the non drive side crank? Or will it be uneconomic to buy one thin enough to fit in? So I might as well buy a crank puller and a lugged (fixed socket) wrench for the crank bolt?

Answer 1

It is definitely adjustable - you'll need to tighten the non-drive side cup, somehow.

The proper way would be to back off the lockring, then remove the cup, and pull it apart, clean and regrease everything, and reassemble here.
Once tension feels correct, you hold the cup still and tighten the lock ring onto the cup to hold it still.

With sufficient leverage, some slip-joint pliers may be enough to tighten the NDS cup without doing anything else. Be cautious to not overtighten if you're doing it this way. You won't be able to use a regular spanner on the hex to tighten it without backing off the lockring by griping the outside knurled section and loosen. Marring the outside is likely but won't affect anything. Or you might get it loose with a hammer and punch into one of the notches.
Simply tightening the lockring won't work because it presses on the BB shell. The problem will be getting a good grip on the thin hex - it's likely a regular spanner will slip off. A deep socket would work well but that requires taking the crank arm off.

Downside of not opening the BB is that the bearing balls may be damaged already and you won't see that.

The long term repair would be to fit a cartridge BB unit instead of loose balls in a cup+cone, but that will need additional tools like crank puller and splined driver thing.

Just remember, making it 90% better is more than it would get if noone did anything. You can make this better, and it would take a lot of work to make it worse. Have a go!