ID: no way to jump to lat/lon location and then know the center point

I want to go to 24.1588841,120.8470812 and put something there.

But there is no way to do it.

Indeed I can search and get
Location: 24.1588841, 120.8470812

but then I have to take a wooden ruler and measure what is the center point of the screen in order to place my point there.

If I am not wrong, JOSM editor has a feature where you can enter a coordinate, and it can create a new node there.

Try http://wiki.openstreetmap.org/wiki/JOSM

Yes in JOSM, see https://josm.openstreetmap.de/wiki/Help/Action/AddNode, see also the link to expert mode on this site

But what about simply putting a marker on the map, without adding anything to the database?
This is discussed at https://help.openstreetmap.org/questions/9669/jumping-to-a-specific-set-of-coordinates-on-the-map#fmanswer
I would like to be able to pop up OCM from a QR’d URL (for example: https://www.opencyclemap.org/?mlat=61.20661&mlon=-149.79245&zoom=18)) and have an actual marker at that point. I suppose I could add points in the DB for every instance I placed a QR code maker on a trail, but that seems a bit of extra work for nought.

As suggested at the help site, http://www.openstreetmap.org/?mlat=53.9027&mlon=-1.2717#map=12/53.9027/-1.2717&layers=C will work.

However if there’s an actual QR code stuck on a post on a trail then you can map that (as what I’m not sure, but it’d probably be “tourism=information; information=something”). The values used for the information key are https://taginfo.openstreetmap.org/keys/information#values . There’s quite a lot of rubbish in that value though. I have a map rendering that tries to decipher these, and the code that groups information values is at https://github.com/SomeoneElseOSM/SomeoneElse-style/blob/master/style.lua#L1263 .

I had same question, and in JOSM, it is ‘easy’ .
Ctrl+J opens a dialog that allows to jump to a position.
Also set the zoom on 0 meters in that josm-dialogwindow.

https://forum.openstreetmap.org/viewtopic.php?id=59750