Trying to understand this oscillator… there’s no emitter grounding or bias

If you wish to avoid holy wars you'll need to avoid making simplistic and incomplete statements :-).

Bipolar transistors are current driven.

MOSFETs are voltage driven.

In both cases the spread of parameters during manufacturing is such that a circuit will almost always rely on feedback to produce a given voltage or current gain.

MOSFETs tend to be slightly more costly at the very bottom end for "jelly bean" applications. But, for switching more than a few ~100mA, MOSFETs are usually as cheap or cheaper than functionally equivalent transistors, are easier to drive from a uC (microcontroller) as a digital switch than bipolar transistors and tend to have very significantly superior on characteristics.

An "on" bipolar transistor exhibits a saturation voltage. This can be several tenths of a volt and to get it much under 0.1V usually requires a high base to collector current ratio that is undesirably high. At 1 A a 0.1 \$V_{sat}\$ (saturation voltage) dissipates 0.1 W and is the equivalent of a R = V/I = 0.1/1 = 100 \$m\Omega\$ transistor. But at 10A the figures are 1 Watt dissipation and 10 \$m\Omega\$. The 0.1V is very difficult to achieve at higher current levels.

The \$R_{DSon}\$ (Drain-Source on resistance) of MOSFETs is typically under 0.1 \$\Omega\$ and you can get devices with 10 \$m\Omega\$ or even sub 1 \$m\Omega\$.

As switching speeds rise MOSFETs need a gate driver to charge and discharge the gate capacitance. These can be relatively cheap.

More soon ....

Simple amplification of audio is the most trivial demand for a BJT and virtually any transistor (including germanium) will do the job you want. Maybe look for BJTs that are referenced as good audio amplifiers but, given that the marketing boys would see some folk being put off buying a particular transistor because it is pigeon-holed by the label.

The level of audio does not need to be greater than 0.6 volts because the right BJT amplifier will set its bias point to accommodate all the + and - swings of the audio signal it wishes to amplify.