As you said, there is nothing that treats the problem. Taking vitamin and mineral supplements (e.g. Nutricap) in the absence of a deficiency is very difficult to advise. In fact, the small studies on zinc, biotin and iron supplements are contradictory. So it is a grey area whether they really help, even if it appeals to the mind. There is a lot of marketing in relation to these products that have a non-negligible price tag.
For serums and shampoos, these are often going to be used to strengthen the hair.
It must be said that a poor diet with little variety is a factor in developing effluvum. So, if your doctor really can't find another cause for your hair loss and it really does turn out to be effluvum, I would focus, first and foremost, on eating healthy with a variety of foods rich in vitamins and minerals. Also, I would try to avoid anything that could further damage your hair (i.e. dye, cold, blow dryer, scented shampoos) and try to strengthen it with moisturizing shampoos and conditioners. If you are taking any medications, ask your pharmacist if they may be involved.
After all of this, if you wish to purchase a supplement, that is at your discretion.