OK. These both have to do with contract status in the future. To reach free agency a player needs a full 6 years of service time. If they end their six major league season with a full 6 years they are a free agent for the next season. If however, they end with 5.9 years, they are still under control of the current club in the arbitration process. A full season of credit is less than a full season (i.e. you can't just hold a player back for 1 game to prevent a full season of service) but 2 to 3 weeks should cover it (I don't remember the exact days anymore).
Super 2 deals with arbitration. Typically a player requires 3 years of service to enter arbitration, but unlike free agency there is not a fixed set of time needed. Players with close to 3 years of service time after their third season will be eligible for arbitration, hence they are "Super 2" since they have less than 3 years. The cutoff date varies based upon the service time of all players in the class. Its usually about mid June but can be a week or two later so July 1st is usually safe.
What does this mean then for a player?
A player debuting in late April 2023 and then remaining in MLB would be under fixed contracts for 2023, 2024, and 2025. He would be arbitration eligible for 2026, 2027, 2028, 2029 becoming a free agent for 2030. Arbitration salaries tend to go 20%, 40%, 60% and 80% of free agent value so the fourth year can get costly for a really good player but its still discounted.
A player debuting in July 2023 and then remaining in MLB would be under fixed contracts for 2023, 2024, 2025, and 2026. He would be arbitration eligible for 2027, 2028, and 2029 becoming a free agent for 2030. So by keeping a player down for 2.5 more months you reduce the number of arbitration years.
What a team should do is really dependent on the projection for the player, if the team is currently competing and the replacements they have. Given the Brewers hope to compete it is likely more advantageous not to wait for Super 2 if they believe the prospect is significantly better than the alternative.
The new ROY changes to the CBA can cause all of these calculations to fly out with players potentially receiving a full year of service time regardless of debut date. ROY is a weird vote since winners can go from solid starters to MVP level candidates. So someone like Frelick who could hit for high average or steal dozens of bases might not win a ROY but could find himself on lots of ballots in 2nd and 3rd place.