Grounding your antenna by bringing up a wire more as 1/4 wavelength does nothing for getting RF off the antenna ground connection, it can even work to add noise.
You should always keep the ground rod wire to the radio shorter as a 1/4 wave on the highest frequency you will work on, otherwise that ground wire will add noise and work as antenna, or form a high impdance path nullifying the earth connection for noise.
Secondly, out of safety, ALWAYS connect your separate radio ground to the electricity ground, so both are at the same potential.
In case of a lightning hit and separate grounds there will de different voltages and currents in both systems causing massive damage.
All my coax cables are grounded just before entering the house on the same rod the radio gear is grounded and the house ground is also connected to there 3 ground rods 10 feet deep.
I should have the lowest eart resistance for miles around with 18 ground rods in my system and 3000 feet radials, as was proven by a check for safety of my house electricity system, the guy never saw such low resistance to earth..
Having a choke with the antenna and a good ground below at the entrance of the house keeps the coax free of RF, add chokes below on the coax to the radio and you did all you could do.
The rest is atmospheric noise, propagated noise from city's and other larger noise sources, neighbours etc.
I spend months here finding all sources of noise from cheap chargers and LED lights, and replaced them with my neighbours.
3 or 4 radials won't matter much the change in signal will be 0.1 dB max.
An dipole has to do with one and still works
The more the better but at a certain point you have deminished returns for all the extra work.
Put it up, use it and have fun.
If you want more knowledge about antennas there is enough on the net or in old fashioned books like I have. ( RSGB, ARRL, Low band dxing etc etc.)
And experiment, you learn the most from that.