In the wml.xml file an infinite context switch between section and error is generated, through lineEndContext: in a line break, the section context sends to error and then this is #poped in the line break, causing an infinite cycle. This causes that Kate freezes.
This is reproducible by typing the [ character and then a line break.
This bug is reproducible only in KSyntaxHighlighting, since in KF5.48 there is no problem. It's probably necessary to add a guard that avoids infinite context changes.
Also, the WML highlighter is a little old and I have seen some problems in sample files. The highlighter considers all content between [ and ] as tag. According to the documentation :
Also, tag and key names follow a special format. They will contain only alphanumeric characters and underscores; in particular, they will not contain +, -, or whitespace.
Considering this, and based on the VSCode highlighter, I modified the code so that only tags with valid names are highlighted.
-  Wesnoth Wiki. SyntaxWML, Tag and Attribute Structures: https://wiki.wesnoth.org/SyntaxWML#Tag_and_Attribute_Structures
-  Wesnoth Markup Language syntax highlightning for VS Code: https://github.com/Byteron/wml , https://marketplace.visualstudio.com/items?itemName=Bitron.wml