How would a hold of distribution of funds for my project impact my application?

The pause in distribution should not impact your eligibility. Three years is an unreasonably long time for an adjustment if your priority date is current. I assume your attorney has done appropriate follow-up. If so and still no results, filing a mandamus legal action may be your only path forward, or wait.

A distribution hold should not affect your case. The reason for the hold, i.e., potential loss of business or future bankruptcy of the project will affect it. Since you have not started your conditional residency period yet, the issues of sustainment of investment and job creation are less important than if you were already in the two-year period, or having to file your I-829 soon. You still must sustain your EB-5 investment at risk, but the job creation window is a bit longer for you, so there is time for the business still to execute its business plan and create the jobs when economic conditions improve.

As long as the project is still active, it should be ok.

A pause in distribution would not impact your pending immigration process. You cannot do anything at this point. You probably should have selected an EB-5 project with stronger financial backing.

Distributions or lack thereof should not impact your I-526/829 case. However, you should check the sub docs to be sure. If I-485 that has been pending for three years, a writ of mandamus is in order.

That will not affect your immigration process. If the project fails, however, then you will indeed have issues with getting your conditions removed. Also, three years of waiting for an Adjustment of Status application? It might be the time to sue.

I do not see how that would have any impact on your application.