I have drawn two spiro curves in Inkscape. Both have the same endpoint, but when zooming in on the connection between these two curves, it does not look fine:

Note the gap between both curves. What I finally want to have is this (simulated using paint):

Getting both curves red is not the problem, but note the rounded edge that I want to have. How can I get this rounded edge? Thanks!

I'd try "Cap" mode in the stroke style tab of the fill/stroke panel.

Thank you, when using the round cap, it indeed works and basically looks like requested in my initial post! I just noted that the curved edge doesn't look as good as expected, especially because only the outer edge is curved.
a) is it possible to also make the inner edge rounded?
b) is it possible to make matching edges, that are not rounded, meaning extend the black line a little bit and cut a little bit of it off, so it matches the angle of the red line? [is there an automatic/easy way to do this. obviously that could be somehow contrucsted manually]

Thanks!

If you don't care about the colors being identical after the joining, you could also join the two paths
(hold Shift + click on them to select both paths, hold Shift and drag a seleciton box around nodes to select both):

Joining the 2 end nodes, as Moini suggested, will make the corner sharp. But then, you can change the Join Style, which is right beside where you changed the end cap style, to make it round or angled.

To make the inner part rounded, will take some work (as opposed to clicking a button or changing an option somewhere). Essentially, you change the line from being a stroked single path to a filled set of 2 paths. If you think you will need to edit other parts of the path, then you should do it first. Because after you do this, it will be much harder to edit. You'll see why, probably easier than me explaining it.

That fastest way would be to start by joining the nodes, as Moini suggested. Then select the path and do Path menu > Stroke to Path. Then switch to the Node tool (if not already using it). Select the inner corner node, and change it to a smooth node (Ctrl + click). Then adjust the handles.

I created a MWE (minimum working example, find the XML at the end of this post) for some visual demonstrations:
Original: 2240 %


Round cap stroke style of black curve:


Make black curve red:


Following the instructions of Moini (danke!):


Stroke Style, Join, Round join, as suggested by Brynn, can be used to get back the round corner :


For my current use case I ended up being so happy with the result of Moinis solution that I didn’t try making the inner part rounded (though I asked for this) as explained by brynn. For my kind of use it seems too complicated to me (and I like the sharp edge), but if that’s the way it’s done in Inkscape, then so it be. Still, thank you brynn for the explanation!
Thanks to everyone who replied here, I am impressed by this support and hope I could give a nice overview of the mentioned techniques here for other readers (except the thing with the rounded inner curve).

By the way, here is the XML for my minimum working example: