Logo switch in a template

Open the Project Flow Chart, expand everything until you find the original logo in the flow chart, double click that logo to open the nested comp containing the original logo, hold down Alt/Option, and drag your new logo to the logo comp to replace the original logo then size is as necessary. If keyframes exist in the original logo comp, you may have to add a null to resize and properly position your new logo.

If there are strokes or other things applied, you'll have to figure out how the animation was done.

Your uploaded AEP does not include all the files, and there are expression errors, so you are probably missing something. I won't do it for you, but if you include the required files, The original logo is in the Logo comp and the file names are Logo1 and Logo2.ai.