Training with a fever isn't a good idea. Minor cold symptoms like a stuffy nose or sore throat sure push through if you feel ok. A fever is a sign of the body responding to fight a a stronger illness and you could still be infections depending on girl load and stage of illness.
Lose valuable time? 2 weeks is nothing in the grand scheme of things. Stay on 2 weeks longer if you're that concerned. If you try to push when your body is dragging from fighting an illness you run the risk of delaying healing and driving yourself even farther behind the 8 ball in recovery than 2 weeks.
To me...
minor symptoms that are annoying but I'm still 80%= train
fever or symptoms that have me < 80% health= rest
Covid= same treatment for any other illness (rest if necessary, hydrate, symptomatic treatment like ibuprofen for body ache, cough suppressant, expectorant, albuterol if necessary.. NO ABX)
Persistent or severe symptoms covid or otherwise= PCP/Urgent care/ER... abx are only indicated with concurrent bacterial pneumonia which you'd be pretty sick and see things like decreased SaO2, chest X-ray consolidation, etc... at which point you'd be admitted and getting them IV