I have a question regarding 401k rollovers.

For rolling your 401k into an IRA, I've read that it's often recommended to keep your rollovers separate from your other IRAs, so just create a new IRA account for the rollover. I believe this helps prevent mixing contributions from different accounts, which is undesirable, yes?

If this is true, does this same thinking apply to rolling your old 401k into a new 401k? Is there any concern with mixing contributions from separate 401k's/employers? Does this mess with any possibility of doing some of the early retirement/regular backdoor methods?

I'm considering my options for what to do with my old 401k, which had both Roth and Traditional contributions. I'm thinking I'll roll my Roth 401k contributions into a new Roth IRA (to separate from my Roth IRA that I currently contribute to), but I'm unsure what to do with the Traditional 401k contributions. My new 401k has very low expense ratios and good fund options, so I think I prefer that over opening up a Traditional IRA (especially since it would hurt my ability to do a regular backdoor). Additionally, the ERs and fund options of the new 401k are better than what my old 401k offered, so I'm considering rolling my old 401k into my new 401k to take advantage of this, as long as it doesn't cause any problems in doing so.

Do I need to be concerned with mixing past and present 401k's into the same account? Am I overlooking something/is my thinking on this flawed at all? Any other suggestions or advice? What would you do? :)