Is a portable Wok burner safe (indoors)

It can be safe - people use gas burning stoves inside on a regular basis.

The one thing you must do is ensure that there is adequate air-flow in your kitchen so as to prevent the build-up of carbon monoxide. This is as simple as leaving a window partially open when cooking.

Another concern would be how stable one of these is on your bench/work surface. Placing a large pan on top of a small foot-print stove will make it decidedly top heavy, so you should get one that is either low and flat (much like a regular cooking stove in a kitchen; e.g. this one) or one with feet that limit the movement/tipping capacity (e.g. this one). I have no affiliation with either product and make no claims about their ability to cook things, other than that MSR is a reliable outdoors brand. After all, you don't want your cooker to tip over and set your kitchen on fire or cause you to get burned from the hot food/pan and/or from the flame.

It is unlikely that a portable propane wok burner is safe for you to use inside. Portable propane burners are ones similar to this model, or one of these. They are high-powered burners that produce a lot of exhaust, and as such can only be used outside or with restaurant-grade ventilation.

However, portable butane wok burners, like this one, are designed to be used indoors. They require only an open window, or a regular consumer-grade stove hood, or honestly just a drafty apartment, as ventilation to use. I have an Iwatani myself, that I use for wok-frying.

I've got a gas stove in my apartment but the BTUs it puts out cannot match a full on restaurant quality wok needed to get that signature 'Wok Hei' smoky flavour (Cantonese transliteration: 'Wok Breath')

I've used a propane torch as a cheap hack to get that authentic flavour alongside a carbon steel wok as described here:

https://www.seriouseats.com/2020/02/hei-now-youre-a-wok-star-a-fiery-hack-for-stir-frying-at-home.html

For minimal equipment required, this hack works surprising well