So I improved the previous script using AWK which is relatively simple when you understand that it handles each line individually in a stream i.e. if you need previous lines keep them in a buffer until you're ready to dump them.

export-binlogs.sh

#! /bin/bash

database_name=$1
input_file=$2
output_file=$3

temp_file=$(mktemp)
sed '/SET @@SESSION.GTID_NEXT=/d' "$input_file" > "$temp_file"

awk '{
  if ($0 ~ "Table_map: `'"$database_name"'`") {
    included=1
    buffer=buffer"\n"$0
  }
  else if ($0 ~ "COMMIT\/") {
    if (included==1) {
      print buffer"\n"$0
    }
    included=0
    started=0
    buffer=""
  }
  else if ($0 ~ "BEGIN") {
    started=1
    buffer=buffer"\n"$0
  }
  else if (started==1) {
    buffer=buffer"\n"$0
  }
}' "$temp_file" > "$output_file"