This is almost certainly one of those interesting topics that will reappear once in a while and I think it's fascinating to see where people stand on this and why they do.
While I understand that there is more nuance in this than "The Byzantines/later Romans were exactly the same as the classical Romans" (especially with how much would be expected to change over the course of an additional 1,000+ years), I can't help but to still entirely disagree with the posters who've made claims that the Byzantines were absolutely not Romans, that the Byzantines have about as much of a claim to being Roman as the Ottomans, Russians, Holy Roman Empire, or implying that the split between the East and West that was done for administrative ease was also done to separate who was Roman and who wasn't. I would think that it's possible to acknowledge the Byzantines as the medieval continuation of the Roman Empire while as wanting to have the Byzantines as their own playable faction for the sake of fun.
Overall, I'm on the fence with this topic.
On one hand, apart from Greece and Macedonia, you could probably make a better case to put the Byzantines and Romans together under one civ than any other two civs that we currently have to work. It certainly wouldn't be much of a blob anywhere near the level of the more questionable ones such as the Celts, Native Americans, etc. Using alt leaders could work well especially if you increased the number of UU, UI, UB, and UD a civ can have so that you can really see the transition between the classical and medieval eras. Or if the game does return to having only a single leader per civ, that one leader could work if it was a leader that could gel well with the themes of both eras such as the aforementioned Justinian, Constantine, perhaps Aurelian, etc.
On the other hand, there are plenty of reasons to want a playable solely Byzantine era faction regardless. Even though the Byzantines were a legitimate continuation of the Roman Empire into the medieval era, there are enough differences that can warrant a distinct civ with fun gameplay (I don't doubt that this can be true for many other civilizations that lasted a long time as well even though the Byzantines are probably the most popular example of this to western audiences). This is especially true to those who are more interested in that time period (thanks CK3) and those who are currently concerned that playing a Roman civ into the medieval era has no guarantees of 'feeling' like the Byzantines or vice versa(even more so if there's a limit on leaders, unique units, etc.). Pretty much the same reason why they split up Alexander the Great from the Greeks, you could group them without feeling like it's overly jarring but it is understandable for a civ more centered around Alexander's themes to those who want and enjoy it.
Essentially, I for one don't mind a separate Byzantine civ and I certainly enjoy playing them and seeing the differences between them and their classical predecessors (and I really like the Byzantine musical themes more than the Roman ones!). I could be on board with grouping the classical and medieval Romans together but that heavily depends on the amount of uniques that a single civ can work with and if they can do a great job of showing the transition between those important eras. I'm currently in favor of the separation but that could change depending on what they do and how well they do it in the future.
I should also mention that I'm also more in favor of splitting up India and China if at all possible.
China is definitely more of a sensitive topic and (correct me if I'm wrong) I imagine that it's unlikely that any of the main dynasties would splinter off from a single Chinese civ without Firaxis losing out on the Chinese market. It pains me to say it but, as much as I'd love to see a separate Tibet and even a Baiyue/Nanman civ, I'm sure that's also unlikely in the current political climate.
Thankfully there's India and and I have some ideas of how it would be split. Personally, I'd like to see it split as India, Chola, and Gurkani. Like with the split between Greece and Macedonia, I have a feeling that a civ named India won't be disappearing anytime soon even if there's a split. I'd think that this more focused India civ would mainly have leaders and uniques from the Mauryan Empire (I'd much rather see Chandragupta and/or Ashoka make regular appearances than Gandhi) though we could hope for alternate leaders from the Gupta and Maratha empires if we want something from a later era covered too. The Cholas look like the ideal choice out of the Tamil dynasties in southern India so I'd be on board with a separate Chola civ. Finally, I'd want a Gurkani civ that covers the Timurids and Mughals and focuses on what they did best. They'd have a significant number of cities in India but they'd also have a decent number of cities in central Asia too.
I almost forgot to mention that I'd be just as curious to see some splitting of the Arabic caliphates between the heartland ones like the Abbasids and the ones in Hispania. I don't know as much about them but it's fascinating to think about!
TLDR, I pretty much agreed with everything that
@Narcisse said!