Electronic – I am looking for recommendations how to lower the noise in this preamplifier circuit

The 220 ohm in series with base of T4, the 100 ohm in emitter of T4, and the rbb' of T4 (internal resistance from bondwire to the actual base-emitter junction) are setting the noise floor. I'd estimate Rnoise (sum of those 3, all affecting the noise across the BE function) to be 1K Ohm, which is 4nanoVolts per rootHertz. [ The DC-feedback 330Kohm is in parallel with 220Ohm Rin, thus we ignore it]

The bandwidth is 250 Hz to 2500Hz. Ignore the 250, and call BW 2500Hz. The total input referred noise voltage is NoiseDensity * sqrt(Bandwidth). Which is 4nanovolts/rtHz * sqrt(2,500) = 4 * 50 nanoVolts, or 200 nanovolts. Input Referred.

Voltage Gain is Rc / Re = 3.3K / 100 = 33. Thus the output noise is 200nV * 33 or 6.6 microvolts, over 250 Hz to 2500Hz. That 33X is also 31dB gain.

The 100 Ohm emitter resistor helps linearize T4's amplification.

I do not see any errors.

It "sounds" like a ground loop or an impedance mismatch, but if everything is properly grounded, then a ground loop seems unlikely, but then again, if everything were perfectly grounded, then you touching anything should have no effect. In either case, a ground loop isolator should help significantly.

A ground loop isolator prevents interference in a ground loop circuit. A ground loop circuit is one in which two or more circuits are connected to the same ground wire. Ideally, all circuits in a ground loop circuit have the same voltage potential. However, if the ground wire has significant resistance and current, the voltage of the second circuit will be slightly lower than the first, causing a voltage difference that makes the ground wire no longer have a ground potential. This is known as interference and can be hazardous, inefficient, and a nuisance in many electrical systems.

Although they are not very expensive, be aware that there are different ground loop isolators for audio signals and video signals, so be selective when shopping.