Is it normal? Yes… and no.

It depends on the ability/quality of the HDR routine and its ability to recognise & correctly handle edges where the overall light level changes rapidly.

A low-ability algorithm will leave this halo to a greater or lesser extent - it's pretty much the trademark of poor HDR. This is an area where modern phones are beating regular cameras hands-down. They can form very well-defined masks to separate these contrast edges & the results are getting close to invisible.

For a DSLR etc, the best way to do this is actually in post, in Photoshop or a dedicated HDR app such as Aurora HDR [which I just learned is discontinued - the functionality has now been folded into Luminar Neo]

Some examples [chosen not by its inspiring subject matter but just because I rarely take photos that include sky;)… The processing was done on a small jpg not the original file, to make the results worse.

Click for full size
Original

Photoshop, with the borders set intentionally high and overall settings to emphasise the bad edges. Clear halo. [Photoshop can do a lot better than this, but is not as good as dedicated software]

Aurora, at default settings, very slight halo

Aurora with intentionally aggressive settings, reasonably acceptable halo for the settings

AI-based algorithms will tend to improve on these results as they are developed further. My versions of Photoshop & Aurora are pre-AI. Newer software is likely to be better still.