Overseeding a lawn: fertiliser, PGR and lawn care after seeding

Hello. I did a search but couldn’t see an answer in the app, so just thinking ahead for within the next wee while when I do a low mow and over seed, etc, do I continue to apply the NZLA products as per the application guide while the seed germinates, etc? I’ll be using starter fert and such at the time of seeding. Also, is it worth doing PGR before doing an overseed (like a week or two in advance?) to help keep the existing lawn growth down while the new grass grows in? Or would that slow down any new growth as well? Thanks