I currently have an elderly Canon DSLR which has served me well, but is time to be replaced. I have three lenses 18-55, 18-250 & 50-500.

I am on my 2nd Sigma 50-500 and both have failed in the same way, the mount gets loose to the point it is impossible to tighten it and the repeated so doing damages the AF. I can get by with my 18-250 for 80% of what I need, but the 50-500 quality is so superior and I really miss that focal length and versatility. It is big and heavy, quite mechanical in its function and I conclude not intended to be used as an every day lens as I do.

I really want to get into video this year and have seen some excellent results with the Sony RX10, specifically the Mk 4. It seems to be acclaimed as the best all in one package camera, so I could kill two birds with one stone in getting this not only for video, but also replacing my DSLR and the troublesome 50-500 altogether. The Zeiss 24-600 lens seems to be pretty decent quality, and while not small, it is about the same size as the Canon with 18-250 and certainly not a bazooka like weapon like the Bigma. But I can't get past that it is an all in one which tend to be jack of all trades, master of none and aimed at high end budget holiday makers rather than aviation photographers, though it does seem popular with birders.

I want to do more vlog style stuff as well as traditional aviation videos, plus maybe podcasts etc too, but also want to take my usual photos. I have already ruled out a GoPro as too restrictive for anything other than travel vlogging and using the video on a DSLR as I run into the same issues with the lenses. The alternate is a camcorder, the Panasonic HC-VX1 seems a decent bet and I am almost sold on this, but I still would need to get a DSLR replacement, which I can do cheaply second hand, but the limit of the 18-250 remains which as I say I can live with, but really want more. However, I don't want to be buying a camcorder, DSLR body plus a lens like a 100-400 L series.

If I am honest, I do not really use my DSLR properly anyway (as in I rarely shoot totally manually apart from at night) and increasingly I find I have barely time to do much than point and shoot semi auto anyway. I have no intention of taking money making photos, or even a.net quality photos, for me, while I like my photos to be decent, photography is more of a hard copy of the siting rather than a hobby or the objective itself. What I am getting to is, this being the case, it seems more than likely the RX10 photos will be of perfectly good quality for what I need - essentially to go on Flickr, web blogs & Facebook groups and for stills inserted in YouTube videos.

Does anyone have any experience with this camera and would it be a significant downgrade on a DSLR bearing in mind my needs?

I think you kind of answer your own question really.

I don't have experience with any of Sony's bridge cameras but I do own one of their MILCs. Quality is generally very good but I don't think it's quite up to Canon's standard, in that I've never been happy with how the Sony renders high contrast edges (even with the sharpness right down to 0). The colour science I also find less pleasing than Canon's, although that's just my personal opinion. However one area in which Sony do excel is dynamic range, which is generally superior to all but Canon's latest mirrorless efforts (although I don't know if that's true of their bridge models).

The Zeiss branding on Sony cameras/lenses is really more of a gimmick than anything else and it certainly wouldn't be enough to compel me to buy. But you do mention that you aren't an overly fussy photographer so it sounds to me like you'll be fine with the RX10. I doubt it has the flexibility of a DSLR and because the lens is fixed it won't have the quality, all things considered — but if you're happy to make small sacrifices here and there, for convenience, it could prove a worthy investment.

If you're primarily going to do video, the RX10 IV seems like a great choice.
The primary disadvantage would be the sensor size. While the RX10 IV sensor is still larger than many other point and shoot/bridge cameras (1" vs 1/2.3"), it will still have a smaller sensor than an APS-C or full-frame DSLR or MILC. Therefore, it would be harder to get good quality shots when there's poor lighting.
The RX10 IV lens has a decent aperture range for a bridge camera (f2.8-f4) but with a DSLR/MILC, you can attach lenses that go as wide as f1.2!

The RX10 series (particularly the IV) is a fine camera, it can do a lot and has good image quality. Its AF is also excellent, but it has one downside: You can't focus while zooming. The zoom motor is also not the quickest to go from one extreme to the other. But in terms of features, it's largely equivalent to Sony's full-frame mirrorless cameras with things like tracking autofocus and capture speed because it has the stacked sensor. What you give up on is sensor size and the ability to change lenses, otherwise it works basically the same.

It's also very discreet and can go unnoticed in areas where a larger camera is more conspicuous.