Nah. Easy fix. Break all the tiles apart and clean off the grout. It should scrape off with a little effort. Then clean any loose dry adhesive off the stair. Get as much off as you can. You can purchase new tile adhesive and a small tube of grout at your local hardware store. Apply a layer of the new adhesive to the stair with a putty knife. Then set the clean tiles in place. They should squish into place but not so much that the adhesive fills the gaps between. Let them sit and allow the adhesive to cure overnight. Then squeeze in enough new grout between the tiles until it’s a bit overfilled. Use a grout squeegee and run it across all the tiles at once to remove the excess leaving it flush with the tiles. Then smooth it all to match the existing with a damp sponge. Remove the left behind haze from the grout after waiting a few minutes. If you don’t want to buy a grout squeegee since this is such a small area use whatever you have that is rubbery and rigid yet flexible like a cooking spatula. Once it dries for about a day polish to a nice shine. Boom done.

My approach would be to chip away any of the remaining substrate that might be loose, scrape it, pick it off, whatever. The goal would be to leave very solid material exposed.

I don't know the equivalent in Europe where you are, but in the US we have Tapcon screws. They come with a masonry drill bit that you would use to hammer-drill several holes along the exposed material. Then screw in the screws until the head of the screws protrudes an appropriate amount to leave room for whatever is needed above the screw head.

These screws now act as a little rebars to support what you build on top. Looks to me like you might need concrete adhesive, little concrete nub mushed around the screw heads, thinset, then tile, then grout.

Also at least here in the US we worry about asbestos. So I would definitely use a true respirator ventilation and filtration. Keeping things wet controls dust very well.

Unfortunately those bullnose tiles are always going to be prone to breaking off because they're jutting out from the stair and are built from materials that are strong in compression, not tension.

Clean the edges and glue them on. Expect them to fail again.

sixtyies

This is totally unhelpful, but I just wantes to say I absolutely love these stairs!

You can try altering the pattern too:

Super easy.
You need a couple of instant noodles packs & gorilla glue.

As others have said, clean existing grout off, adhesive, and grout it again. It will be discolored.

Were you looking to retile and regrout the area or glue it back into place?

https://thistothat.com/

You can try sika 11fc.

Update: I finally fixed the stairs by glueing things back on with flexible tile glue and finishing up with the thing you use to put in the groves between tiles. It seems sturdy until now :)