Tuitrans does luggage transfer town to town in Portugal. Caminofacile does town to town transfers from Porto to Santiago.
Just a note....the biking from Coimbra to Porto can be somewhat grueling. We biked in September and found it to be much harder than we expected. It is very hilly - not mountains, but some sizeable uphill rides. If you want to stay off the main roads - which we did - you need a mountain bike in many of the areas between those two towns. If you're okay with road biking, you might be okay, but even when we were on the roads, it was hilly. I tried to attach one photo as an example, but I'm not sure it uploaded.
Anyway....you might be perfectly okay with it. We're planning to ride the Camino again next September, but we're going to start in Porto and ride the Senda Littoral......that is lovely!