You can set your laptop to not sleep/hibernate. Alternative to that, if you're on Windows OS, is to run ASF with --system-required command-line argument (check wiki for more details), which will hint Windows to not go into sleep/hibernate for as long as ASF process is running, and it'll automatically allow it to do so once ASF stops working.

Where exactly you run ASF is your own choice. The cheapest way to do so if you calculate long-term savings, is to buy cheap ARM-based mini PC, such as Raspberry Pi Zero 2 W (which normally costs around $15), and run ASF there. Power consumption of such setup should be within 100-300 mA. Assuming higher value, that's 1.5W, which equals to around 1.08 kWh per month, running ASF 24/7. Taking into account electricity costs in Poland, such setup would cost you $0.20 in electricity per month. Considering the fact that in normal stationary PC you typically won't bring electricity lower than 100W in idle, and laptops will typically take at least half of that, the entry cost ($15) of the raspberry pi will pay itself within 1-2 months, maximum 3 if you had some super power-efficient laptop with 33W or less in idle. So 3 months in, and you have a machine for free from electricity cost alone - and if you have more expensive electricity, it'll be even faster than in my example.

Whether or not you want to go for such a setup is your call. Additional value is that you can run more than just ASF on such machine, but downside is you'll need to dig a bit and educate yourself how to do all of that, which might not be feasible, especially if your time is not free. Still, even cheapest VPSes won't offer running ASF for $0.20 monthly or less, the only better option would be to find a service allowing you to run ASF for free, which as you can guess, is either hard or outright impossible to do, and even if possible, always comes with some strings attached.

I'm running ASF myself on my Raspberry Pi 4 - a bit more power-hungry, but also more performant machine, which still doesn't consume more than 5W monthly, being only 3x higher than above, while still being 20x less expensive than idle PC, and around 10x less expensive than a laptop. Such option would be best if you wanted to also run other things than ASF on it, and you have a lot of possibilities in this regard - but if you want something just for ASF, Zero 2W variant is probably the best.