I've never seen JPEG artifacts on images modified/saved 5 or fewer times. Viewing on a monitor including at 100%, printing photos, whatever - in practice the artifacts don't matter.
jpeg artifacts mainly show up on drawings. where they seriously degrade masking operations. which is a hobby of mine. so I always appreciate it when a drawing is a png. rather than a bunch of jpeg goop.
JPEG artifacts are less disturbing because they're so obviously artificial. WEBP and similar artifacts look more natural, which makes them harder to ignore.
For non-photographic images, I'm horribly sensible to the ringing artifacts. Thankfully, there's waifu2x (in denoise mode only) to remove those when textures don't confuse it too much and I use MozJPEG to encode, which really improves the result.
There's something to be said about this. A high quality JPEG after cleanup can sometimes be larger than an ARW (sony RAW) on export and it makes no sense to me.