Hold on the horses! It won't work or at least not satisfactory. I told you already X times how measurement microphone (like UMIK-1) is a key to see what happens and to be able to focus on fixing it. Secondly you need DSP which can make desired changes and preferably to any input source you might or might not want to use. With local reproduction it's easy. You need Foobar 2000 and room EQ for it.
Professional Audio Plug-Ins
mathaudio.com
From Windows PC of course and with two chenel DAC. If you want that it applies to all sources that you can play on PC then you need JRiver with WDM intermediate driver and you also get equal loudness normalisation (ISO 226 2003), good embedded plugin suport, volume controls, remote app support (JRemote 2 also paid and not very polished and abandoned) convolver ain't good (lags a lot) but you use plugin VTS one instead and so on.
If you want to be able to possibly expand setup one day then you need multichannel audio card or interface instead of stereo DAC. If you want self stand DSP then MiniDSP Flex but you don't have money for it.
First you buy speaker and microphone and see what and how much it needs to be corrected. You can use even MB audio out for the purpose and until get something better (for the time). If you can pass with cuple of PEQ filters then something like WiiM Pro Plus streamer (with all streaming services, DLNA and inputs it supports) might be good choice (stereo only). Hopefully they will increase number of PEQ's from only 4 currently (and separate per chenel).
BT is lossy and with very limited range especially on high bit rare more quality codecs like LDAC. WiFi is much better and lose less.
Remember Rome whosent build in one day.