Managers can make a huge difference imo. Look at teams that overachieve given their budget and the squad that they have. Of the current premier league managers I think Eddie Howe, Tony Pulis, Marco Silva and Rafa Benitez are all examples of managers making a difference. Bournemouth probably wouldn't be in PL without Eddie Howe, and the other three would struggle to compete without their respective managers. Sure, some managers spend a lot of money to be successful, but I still believe they are excellent managers. Imo part of being a good manager is identifying the weaknesses in your squad and having an idea of who you want to sign to fix it.
Also, if there was ever an example of a manager making a difference it would be SAF. Yes he spent quite a bit of money for his time, but in the latter years he had less money than Chelsea and City and also had to contend with European powerhouses like Real Madrid and Barcelona, yet United continued to be very successful. Some of the performances he got from what might be considered average players by United's standards was incredible.
This is the same Bournemouth that was fined 8Mil for breaking financial fair play to get into the Premier League right?