lme4 was able to fit all the models. This is partly because I featured this package to fit this class of models in my Extending the Linear Model with R where I avoided covering models that lme4 could not fit. Nevertheless, lme4 is capable of fitting a wide range of models. There is the problem of inference which lme4 chooses to avoid but lmerTest does a convenient job of testing the fixed effects for LMMs. You need to work harder to test the random effects but one could argue that the random effects reflect the assumed correlated structure of the data so there is no benefit in testing them (at least not for the current data). If you have a GLMM (i.e. a non-Gaussian response) then the inference gets harder.

nlme has the advantage of being part of the standard distribution of R which is great when you are sharing or collaborating because you can be sure that the other party has nlme installed. This is a big advantage when dealing with inexperienced R users. Furthermore, it's a very mature package that's been extensively tested and is very stable. (lme4 is also mature and widely used but nlme even more so). nlme can fit some models that are unavailable in lme4 that have correlated error structures of various kinds. It also can fit GLS and some non-linear models. But it cannot manage some models that lme4 can handle such as crossed effect models (at least not without some unnatural manipulations). It's also slower for larger datasets although this speed difference was not important for the smaller datasets considered here. Furthermore, it cannot do GLMMs. It's also less cautious about inference than lme4. Sometimes the results will be OK but lme4 + lmerTest is a safer bet unless you are very well-informed about LMM inference.

I was curious about this package and thought this would be a good way of discovering its capabilities. But now I realise that it is special purpose software built by those interested in a particular type of longitudinal data commonly arising in clinical trials (although it can be useful for data from other sources). It was able to fit some of the models here but it just was not designed to handle many of them. Like nlme it has the capacity to model correlated error structures. It is more capable than nlme in this respect and has better inferential tools. If that's what you need, then mmrm is for you but it's not a general purpose package.

Again, I tried this package out of curiousity but now realise that I did not understand its purpose. For the models considered here, it gives essentially the same results as lme4. It's less well connected to other packages such as emmeans and lmerTest and it's harder to install. I did not discover any additional capabilities for the models fitted here. The strength of glmmTMB is in fitting less common response types, such as the zero-inflated Poisson. If you need to fit such a model, then glmmTMB is for you. It also promises to fit faster than lme4 for some combinations of data size and model. This was not an issue for these examples but perhaps may be useful in bigger problems.

There is a wide selection of packages that can fit some smaller subset of GLMMs but nothing with particularly general capabilities. If you want to take a Bayesian approach, there are some widely capable options such as brms. It's also easier to fit your own custom model in Stan (or other general purpose Bayesian software).