Why does my DIY "solar panel circuit" show battery voltage and not solar panel voltage?
If you connect the voltmeter leads to the terminals of the battery, you will read the voltage across the battery.  There really isn't much more than can be said about that.

The battery is essentially modelled as an ideal voltage source in series with a relatively small resistance.

The solar panels, on the other hand, are more like a current source in parallel with a relatively large resistance.

When the solar panels are connected across the battery, a simple model of the circuit is







simulate this circuit &ndash; Schematic created using CircuitLab

The current \$I_{sc}\$ is the short circuit current produced (for a given illumination) by the panels when the panels are short circuited.

The voltage \$V_{oc}\$ is the open circuit voltage produced by the battery when the battery is open circuited.

Elementary circuit analysis tells us that the voltage across the battery terminals with the solar panel connected is

$$V_{bat} = V_{oc}\frac{R_p}{R_p + R_b} + I_{sc}R_p||R_b$$

Since, typically, the resistance \$R_b\$ is much less than the resistance \$R_p\$, the voltage across the battery is approximately

$$V_{bat} = V_{oc} + I_{sc}R_b \approx V_{oc}$$

In other words, unless the panels are providing a relatively large current and / or the internal resistance of the battery is relatively large, you will measure approximately the open circuit battery voltage with the solar panel connected.