Can a vase of flowers and glycerin water placed on a cabinet with birth control pills increase the humidity of the air too much?

If without a vase with flowers in your apartment there is an air humidity of less than 70%, then the vase will not make it rise to 70%. I have no knowledge of your humidity, so I will not assure you that it is certainly less than 70%. You can check this with a hygrometer.

So if I store tablets in a closed cabinet in a room (not in the bathroom or kitchen) at a temperature of about 21 ° C, the humidity of the air will not reach 70% through the water next to the cabinet with tablets or the air from the bathroom next door?

No, holding a vase of flowers with water and glycerin does not affect the increase in air humidity to such an extent that it interferes with the proper storage of Vibin. The relative humidity of the air in the place of storage of drugs should not exceed 70%. I encourage you to buy a hygrometer if you are afraid that it may have exceeded this value. The general guidelines for proper storage of medicines say that most medicines in the form of tablets, capsules and ointments are stored at room temperature, i.e. between +15°C and +25°C. For Vibin it is up to 30°C. I am attaching a study that may be helpful: https://www.gdziepolek.pl/artykuly/jak-przechowywac-leki