Why does this Regex pass on Bash 5.3 but fail on Bash 5.2?

I think you're seeing the result of relying on undefined behavior. { is the regexp metacharacter that indicates the start of a repetition expression, e.g. foo =~ fo{2} so it's not obvious what you were hoping that "\{" =~ { would mean. If you meant it to match a literal { then use a regexp that is defined to mean that, i.e. "\{" =~ [{] or "\{" =~ \{

Instead of putting regex as is in [[ ]], without quotes, it's much better to define a variable, like

regex="{"
[[ "\{" =~ "$regex" ]] && echo "true"