You somewhat can - go to Settings -> Import/Export Settings -> Export as a JSON file and Import after you make a new account elsewhere. DMs and anyone following you won't be redirected to the new account, but your community subscriptions and block lists will be transferred this way. Repeat as often as necessary:-).
Lemmy.zip seems an okay instance, or at least I cannot recall anything bad about it. Although it doesn't defederate with any of the big 3 so it's totally up to your personal efforts to avoid being trolled by users from hexbear.net, Lemmygrad.net, or Lemmy.ml (2 of those 3 are defederated from most large Lemmy instances, so lemmy.zip is a bit unusual in that regard).
I suggest at least checking out PieFed: the experience with the sign-up wizard alone is likely enough to convince you to stay, e.g. you can choose to filter All/Some/None of posts containing keywords "Trump" or "Musk" (if you wanted something like that:-), and it asks what topics you are interested in and then subscribes you to communities based on those answers, rather than leave you to have to discover and sign up to each one individually on your own.
Edit: Or even without an account, and even if you plan to stay with Lemmy, the categories of communities (pre-defined "Topics" and user customizable and shareable "Feeds"), e.g. see in action on PieFed.social, are really cool! π Like multi-Reddits (I hear, I never used those:-) they both aid in community discovery and helping to separate our your interests, like you might not want to actually "subscribe" to any political communities so that those topics don't show up in your Subscribed feed, and yet still you can read about that topic anytime you want by visiting News and Politics - so you really can both have your cake and eat it too! π π°π
Or for someone located in the USA (low latency ping) looking for a general-purpose Lemmy instance I highly recommend Discuss.Online, especially for a new user coming over from Reddit - it has fantastic uptime and very friendly devs who fix and improve things quickly:-). And it defederates from hexbear.net and Lemmygrad.ml.
Lemmy.zip is the #12 instance in terms of Monthly Active Users, so indeed a good choice in that respect - not too small or too large but in the middle:-). And a great choice for someone who exclusively loves gaming and chooses to pursue that interest by browsing Local rather than All.
Still, it is always good to know what options are available to someone:-).
Lemmygrad.ml also appears in that list, although unironically of the big 3 instances, that one I actually respect due to the honesty of their label:
Someone reading that could either become enthused or conversely nope out easily, it's when the label doesn't match that causes the vast majority of the problems.