Is it a good practice for teaching assistants to sit in the lectures?

I have seen TAs do this, but generally don't ask my own TAs to do it. As you say, it's a (very) time-consuming way to solve the coordination problem. I personally prefer to just sit with the TAs for a few minutes (< 30 minutes) every so often to coordinate, which in my experience has been completely adequate. Of course this means that I have to invest a little of my own time, but I find it completely appropriate to invest a few minutes of my own time every so often to save my TAs quite a lot of time - but of course your milage may vary with other professors. I certainly wouldn't find it strange if a TA sat in the lecture, I just don't find it necessary.

However, I do strongly suggest that the TAs take some time to go over the teaching material, so that they get a sense for what I am covering in the lecture, and how far I have gotten by the time their tutorial or supervision session rolls around.

Finally, we have also used a joint Slack channel where TAs can ask questions and expect a fairly immediate response. This has been useful for me to communicate if I, for instance, needed to skip a section due to time reasons, or if I felt through in-class exercises (or blank stares) that a certain topic needs deeper exploration in the supervision sessions.

I have been a TA myself, and I can highly recommend doing that. I had been facing the same problem as you (In my case, I attended the same course before joining it as a TA, but it was restructured in the meantime) and it really helped me to understand the lecturer’s concept and the connections between single course elements.

While this may vary from discipline to discipline and country to country, at my university in Germany it is good practice to attend the course you assist with and not regarded as strange, neither by the professor nor by the students. In my department, it is just common to see the teaching assistant(s) among the students in the lecture hall and viewed as totally normal, from both the professor’s and student’s view. If you’re unsure however whether this applies to your department as well, I guess it is totally fine to ask the lecturer.

In addition, I can relate do Buffy, there is never a reason not to attend. It helped me to gain a deeper understanding of the course content and besides, I learned quite a lot from the professor.

It is good but not usually essential that you attend lectures, but it can depend on the field. If your only task is grading the course, it probably isn't very useful, but if your task is to actually interact with students it can be worthwhile if you have the time for it. You may not need to pay the same attention while there that the students do, of course, if you are already familiar with the material.

One reason that it is good if you intend a career in academia is that you get to see some other professors and how they work with the material and the students. This can help form your own teaching style.

However, outside mathematics and the sciences it may be more important to attend lectures, at least occasionally. In a Literature course, for example, you may need some way to know what the professor is saying about a book or genre for you to be able to be effective.

But there is, IMO, never a reason not to attend, if you have the time. You might even learn something or deepen your knowledge of things learned long ago. That opportunity to "think back" on things can be valuable even if you have already formed an understanding of them.