Reddit reviews Portable Gas Stove & 2 x Marksman Gas Refill Cartridges 227G [Misc.]

>a very small battery ...

You mention 30V, which probably means a 60-cell panel, that are usually >240W, delivering a (max) current of >8A.
Assuming you want to use lead-acid (which like a C10 charge), AND the charge-controller is PWM, then the battery should be ~80Ah, if the charge controller is MPPT then about 160Ah.

Using both grid-tied inverter and charge controller at the same time doesn't really work, if it's PWM it will draw the panel voltage down to 14V-ish which is probably too low for the grid tied inverter (assuming a 12V battery system), an MPPT controller will fight the grid-tied Mppt controller.

A small microwave is 700W, from a 12V battery that draws 700W/12V=60A, if the battery is 80Ah that is a good way to destroy the (deep cycle) battery.
If that is only to boil water then a 12V submersible heater that draws 10A is a better choice for an 80Ah battery.
Or get a small gas camping cooker that can also heat up your food.

There are 12V car laptop chargers.

Lights:
As an alternative, a (few) USB powerpacks with 'strip' lights (light angle ~100⁰ for desk work), or USB led bulb (very large angle), or USB torch (narrow beam, battery included).
Note: those LEDs are 'cool' white and low power.
These 7-60V buck USB chargers can be connected directly to the PV-panel in parallel with the grid-tied inverter.

https://www.amazon.co.uk/Portable-Camping-Cooker-Cartridges-Refills/dp/B000RHV3MU/ref=pd_zg_rss_ms_lp_outdoors_9

something like this, can make tea plus infinite other foods and is way easier than an electric setup in the van.