In general, the compensation is much less than engineers at the same level but the potential for career growth beyond senior is much easier.

I would agree on the junior side of things. There is a higher threshold for the starting line for engineers, but for higher levels, design is by no means seen as a less prestigious role. Not in any sense of the word.

For salaries – see e.g. levels.fyi for quick comparison. Even Google – a company not really known for valuing design that highly: SWE L6 avg. = 520K USD. Product Designer L6 avg. = 515K USD.

Yeah no argument on prestigious, just noting the comp differences.

I won't speak on engineering vs design. but compensation doesn't necessarily correlate perfectly with prestige. Teaching is the easiest example in the opposite way.