OK. My first suggestion would be to not take the mean of the ratings and rather use the raw data and a hierarchical model to account for multiple observations from the same person. (i.e. a random intercept per person)
I agree that an ordinal model with 201 levels could be a stretch (though @betanalpha has a nice new case study about setting priors for ordinal models when some categories are sparse). But you could still give it a try, I would not be surprised if it works.
If you don’t want to try the ordinal model or it indeed does not work, you can try a beta-binomial model, because the beta-binomial distribution is for integers with a lower and upper bound. Here is a description of how to implement a beta-binomial regression in brms.
Finally, you could also check out a model for censored data (e.g. using a gaussian model). If this makes sense depends on why you have so many responses on one boundary. Intuitively, this would be a good model if the reason you end up with many values at 200 is that your scale has a restricted range. (see here) for a quick into into censored vs. truncated data.