Since no one answered yet I'll provide a few numbers from Bloomberg's OVML as mentioned in a comment. The following logic is used by Bloomberg:
The Heston model parameters are calibrated to at-the-money and
25-delta options, with time-to-expiry between three months and one
year. When calibrating the Heston model parameters to fit a volatility
surface, mean reversion parameter is fixed to a typical value, due to
an inherent interplay of opposing roles between mean reversion and
volatility of volatility.
EURUSD for example looks like this at the moment.
A few pretty much randomly selected values.
With regards to the sign of the correlation parameter, the Brownian motion that drives the variance process is correlated with the spot process – therefore, the correlation coefficient for the inverse spot will be the negative value of the original one.
In OVML, the Stochastic Vol model is a degenerated SLV model. However, it is not using using Heston dynamics because of the following explanation on the help page:
We have chosen a lognormal process for the volatility process, as
opposed to the familiar squareroot process found, for example, in the
Heston model. We get more realistic behavior for the paths of the
volatility process and for the dynamics of the volatility surface.
Looking at SV, you will see the following (time dependent) values.
Pretty much the same applies to DLIB, where typically short term correlation and vol of vol is higher and reduces with tenor.
Although it is just a few snapshots, I hope this helps a little bit.