There's nothing wrong with your model. This is a combined consequence of very high among-ID variation and Jensen's inequality. Looking just at glmer results (since the results are similar across platforms), the intercept is 7.323 and the among-group standard deviation is 9.645.
The inverse-logit (logistic) of the mean prediction is not the same as the mean of the inverse-logit of the predictions ...
mean(predict(fit_lme4, type = "response"))
[1] 0.7468441
plogis(mean(predict(fit_lme4, type = "link")))
[1] 0.9840272
There are various ways of handling this issue. emmeans in particular has some Delta-method machinery that can be used.