While the result is paginated, there's a clickable element that copies ALL tag names to the clipboard. This is most likely what's overflowing.

final String allElementNames = names.get().sorted().collect(Collectors.joining("\n"));
...
.withClickEvent(new ClickEvent(ClickEvent.Action.COPY_TO_CLIPBOARD, allElementNames))

Confirmed. As @HenryLoenwind shows, the /neoforge tags commands have a feature to copy all items across all pages (for listing tags of a registry, tags of an element, or elements of a tag) to the clipboard. For a huge amount of tags, that click event text exceeds the limit for encoding strings in packets.

I think, to keep it functional for most use cases but handle obscenely large lists, we will simply limit the copy-to-clipboard text to some reasonable limit of entries (with a message that it is a truncated list at the start and end). Assuming a size of 32 characters per tag key, that fits about 1,024 elements, which we'll just round down to 1,000.

Perhaps we can consider a new /neoforge dump sub-command for specifically dumping tag-related entries?