How rich was Jekyll exactly?
Pretty wealthy. He had a lavish house with multiple servants and that quarter of a million pounds listed in the will is roughly the spending power of 40 million British pounds today or 50 million USD.
That was also why he was so worried about his reputation, he was in a social circle where everyone had eyes on him and he was subject to a lot of scrutiny. Someone in Jekyll's profession and social circle would have been expected not just to be respectable but to actively be a pillar of the community and would have been expected to maintain the social hierarchy, contribute to "worthy" (i.e. socially acceptable/fashionable) philanthropic causes or charitable organizations, and to always be on top of social etiquette. No scandals, no crude behavior, no being seen in seedy, low-brow, venues like music halls, no hanging out with people beneath your status lest you lose your place in high society.
And the creation of Edward Hyde does require that Jekyll be of that social class, either an aristocrat or just beneath in terms of wealth and status. Someone at the peak of a career long earned, well known and well respected enough that if he were caught in something dodgy the whole of London would know.
And that's why Hyde has the reaction he has when he's threatened thus:
"He was the usual cut and dry apothecary, of no particular age and colour, with a strong Edinburgh accent and about as emotional as a bagpipe. Well, sir, he was like the rest of us; every time he looked at my prisoner, I saw that Sawbones turn sick and white with the desire to kill him. I knew what was in his mind, just as he knew what was in mine; and killing being out of the question, we did the next best. We told the man we could and would make such a scandal out of this as should make his name stink from one end of London to the other. If he had any friends or any credit, we undertook that he should lose them. And all the time, as we were pitching it in red hot, we were keeping the women off him as best we could for they were as wild as harpies. I never saw a circle of such hateful faces; and there was the man in the middle, with a kind of black sneering coolness—frightened too, I could see that—but carrying it off, sir, really like Satan. ‘If you choose to make capital out of this accident,’ said he, ‘I am naturally helpless. No gentleman but wishes to avoid a scene,’ says he. ‘Name your figure.’
That kind of threat, described as the next best thing to killing someone, shouldn't frighten Hyde. Hyde is a nobody from nowhere.
I've pointed out before that the language an author uses is often deliberate and I believe Stevenson's framing here is equally intentional. When he positions the death of reputation as next to the death of the subject themselves that's not hyperbole. Back then social ostracization could kill a career, make a whole family untouchable and the stigma would follow possibly for generations. The higher up on the social rung you were the harder you'd fall.
Also side note: I do really really LOVE Stevenson's prose, it's so fun he's so colorful.