Plotting VV and VH in the time-series tool is easy, you can select the polarization with the filter option.
Technically, it works if you compute the ratio (VV/VH) per date in the band maths and name the bands accordingly (e.g. starting with ratio_ and then add the date as in the other bands, such as 21Jul2021)
We have discussed and achieved this for NDVI computed from Sentinel-2 data here: Time Series (Temporal) of NDVI
However, this is prone to errors and hard to debug if something doesn’t work, so maybe it is easier to create a stack of all dates, then calculate the ratio per date and then use the Pin Manager to extract all values among a certain point to CSV and make the plot in MS Excel, for example. This gives you more control about which data is displayed and also more option regarding the visualization.