Users on private beta sites already have a plethora of privileges that they wouldn't usually get for several years on other sites in the SE network, such as being able to access the close-vote review queue. But being able to have more than 20 pending edits at a time is not one of them.
I think it is unlikely that the SE staff will make many changes to the already-established process for private beta sites, for a number of reasons. One of those reasons is that in each of 2020, 2021, and 2022 we have had only 1 or 2 private beta sites launched per year, which means that private betas happen rarely, so it's not very worthwhile for the SE developers to spend energy on changing any code. Another reason is that private betas last for 2-4 weeks, which again means that any inconveniences we experience during this time are very temporary in the grand scheme of things. There's more reasons I can write, but in this specific case of wanting to increase the pending-edit limit, only one user has made more than 7 edits, so again it doesn't seem like something for which SE will want to devote a lot of resources. Last but not least, the reason you have so many pending edits is because you're the only one editing the tag wikis, and maybe it's good to limit this a bit because otherwise all tag wikis will be written by the same person.
I am only speaking for myself though, and if SE staff do want to give more privileges to users of this private beta site, then I have no problem with that!