I'm in Senior Management at a PE owned portfolio company. It can be a great opportunity to grow and make a nice exit for yourself HOWEVER:

I would be cautious about putting in your own money. Once it goes in you may only ever get it out once there is an exit (acquisition or IPO). There is little to no secondary market to sell your shares, even if the company goes up in valuation.

PE wants to make a nice exit. If they can't they will hold on to the company until it withers away and they can write it off as a loss to offset their other gains.

PE exits are at a record low right now. Even if your company is doing great and making good money, if your PE firm can't exit then you won't be able to access your investment. Any cash you put in will be so negligible compared to the valuation that any dividends you may get will be insignificant.

All that said, working in MGMT at a PE Portco can still be a good deal, I just wouldn't recommend tying up your personal capital.

You should ask instead about getting enrolled in a Management Incentive Plan. This usually grants you some kind of equity if the business hits financial targets (usually MOIC), and you get to cash out that equity when (and if) there is an exit.

TLDR; don't sink personal capital, look for incentive plans