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Consider the following Posix RegExp and search text:

Regex: [a\]]+
Text: baa[aa]aab

I would expect the regex to match aa]aa, but for some reason it matches a] instead. I think it's because TextPad doesn't recognise \]. If this is the case, then it's a bug.

Does anyone know how to solve/workaround this problem?

This is not a bug. Some regex recognisers treat a backslash in a character class as an escape character, some don't. TextPad's regex recogniser doesn't. Use
[]a]+

and it is documented
Help - Help Topics - Reference Information - Regular Expressions
then scroll down to Class expressions.

It says under Simple Characters:

To match a right square bracket (]), it must be the first character of the class expression, after any initial circumflex (see Negated Class Expressions).