MacBook Air 2020 Intel T2 stuck with Internet Recovery and possible bad battery

I need some help to revive a MacBook Air Retina / Intel, early 2020 (T2 chip). I bought it from the former owner, who did not use it for a year, and the machine did not start anymore. I finally managed to start it up in safe mode after charging it overnight, NVRAM and SMC reset, with the battery warning sign visible. The mouse was moving very slowly over the screen. It could not normally start. As I could not lock in, I finally put it in DFU mode and managed to make a restore from Apple Configurator 2 with an iMac (MacOS 12). It now starts only in Internet Recovery mode. When I have to choose the wifi network, it gets stuck after password entry, with an endless spinning wheel. The fans run at high speed and mouse behavior is very sluggish. Even after hours, no progress. The machine is cleared off from iCloud by the former owner. I ordered a replacement battery from a 3rd party vendor and it has exactly the same behavior. The machine gets off immediately after I unplug the power cable. I managed once to start Internet Recovery in Ethernet mode. With a USB C > USB A dongle and an apple USB A > Ethernet dongle. For the first time the progress bar appeared and showed progressively up to 24:00 (min) before getting stuck again. Questions: Diagnosis ? Bad Battery only and bad replacement battery? Or other hardware issues? Any chance that the battery and speed problems resolve after internet recovery? Therapy? Another replacement battery? The vendor is not so willing to replace it. I wanted to retry internet recovery again with ethernet, ideally buying a Thunderbolt 3 > 2 and a Thunderbolt 2 > Ethernet adapter to make this work best.