Typically, in private union shops there is a check and balance between union demands and the viability of a business. Meaning, if a union gets too greedy they create a threat to their own existence by potentially driving their employer out of business. I witnessed this in the automotive sector when unions had to renegotiate their rates in the aftermath of the financial crisis. Workers brought in afterwards were often making less than half of what they would have made if brought in before renegotiation. I don’t think that same check exists (or is at the very least slower and weakened) in the public sector because the govt is a monopoly and can often raise taxes. Sure citizens can try to elect politicians that buffer this but at best it’s a process that takes years to enact and at worst is ineffectual. Because they have a captive “customer” base and a “company” that can’t go out of business, it provides a theoretical avenue for extortion. Besides all of that, civil servants are intended to serve the populace (hence the term servant) and not be strictly motivated by personal gain; they generally take an oath, meaning they are expected to answer to a higher calling. (I also have lots of reasons to believe public unions are beneficial but like I said, just wanted to potentially give a side you weren’t familiar with)
Regarding PPP, there’s been some good links in this thread that show public sector unions are quite strong despite the dwindling private sector unions. Meaning government policies are not enacted devoid of union influence. High level policies will almost always be driven by political appointees so I have doubts that an even more unionized public sector would impact on these policies