Copy cell data from one worksheet to another worksheet only if both worksheets unique value matches

This can be done easily with XLOOKUP (Or with VLOOKUP if you're using an older version that doesn't support XLOOKUP).

On Project C, you should use the following in the column with the description you get from Project A:

=XLOOKUP($A2,'Project A'!$A:$A,'Project A'!$B:$B,"Not found")

Where:
$A2 is the reference for the unique value (Preferably within the same row of this cell);
'Project A'!$A:$A is the range of the unique values' column on Project A sheet;
'Project A'!$B:$B is the range of the descriptions' column on Project A sheet;
"Not found" is the text that will appear if the unique value is not found on Project A. This is an optional field - you can leave it empty, so if the value won't be found a #N/A error will be the result of this function instead.

Another neater way of using the same function, is with named ranges - using Tables. Define the data tables on each of your sheets as Excel Tables by selecting them and pressing ctrl+T or Insert -> Table.

Now, you can rename each table (let's say - tblProjectA is the name of the table in Project A) and use its name and its columns' header name in the function (let's say that the "unique value" column header is "ID", and "Description" is the header of the description column in tblProjectA):

=XLOOKUP([@ID],tblProjectA[ID],tblProjectA[Description],"Not found")

Here's an example:

These are 3 sheets for example -

While this is the actual formulas written in Project C sheet: