Yes, it is a WL. Coarse focus is the same on both. I have peeked inside to see that fine focus on GFL has a few gears on the 'floor' of the housing which are connected to the spring on the front somehow. I cannot see that on pictures of WL, that part does look delicate but there was no need to touch it. It works perfectly, so I took your advice on not touching it. But I think if it starts misbehaving it is best to repair before something breaks.
If the gear lubrication is the only problem, I think one could try to clean without disassembling.
The shaft connecting 2 fine focus wheels is the same on both scopes. The front part where the stage holder connects is smaller on GFL but I think it is very similar. I think one could be able to get it right with enough time, patience and caution. The main problem is that any parts for this scope are seldom found and/or too expensive.
After doing all this I think I won't need to touch it for years...
Hobbyst46 I suppose you might know all this but I'll write for reference of the ones who don't. As I didn't know a month ago and couldn't find online.
Fine focus has limiters so you don't go too far up or down. There is a bolt on the shaft which moves until it reaches the limit. If you turn the fine focus to the end on either side to reach the limit and after turn the big wheel together with the fine focus wheel in the same side, the limit will also move and then the fine focus goes too far. This can result in the whole fine focus / stage / condenser assembly falling down and bumping quite hard to the floor.

Nothing bad happens, but it was a huge shock to me when it first occurred some time ago. I was certain I have ruined everything and after looking inside I thought I saw a tilted gear

Later I realized it was all in order

My son was so angry, he was shouting: "I knew you'll ruin it. It was good when it got here, whyyyy!"
After that happens the limits are no longer positioned right, so they need alignment again. You can feel that when the fine focus end is not a sharp tick but has a mellow feel of the spring strain. It is visible on the image when on the end of the focus range the focus doesn't move. It can be aligned again by turning the fine focus the other way around and then turning both the big and small wheel together in this direction to go over the limit again on the other side. Then going back and checking if the tick is back and repeating the process if needed... If completely falls, you need to repeat maybe 6-7 times.
It is easier when the microscope arm is removed as you can then move the big wheels as much as you want and you can see the limiter bolt coming and going...