I haven't solved the problem, but I have done some troubleshooting. However, I don't have the time or energy to pursue it further right now. I have an old Mac with a Windows partition, so sometimes when older games don't like to work with Wine, I'll just use the old Mac - for me, that is the easiest solution, at least for now. (I really want to retire that old Mac and free up the space that it occupies, but there always seem to be a few older games that persistently refuse to work with Wine.)

Just in case it helps others who are trying to make this work, I'll post my findings here, and maybe somebody will get a good idea from this and will figure it out.

Basically, I think it is a audio/video codec problem. This is a common issue with older games - audio/video codecs are quite the nuisance, especially in the late 1990s-late 2000s period. Sometimes, games use weird or non-standard codecs and/or the video files are corrupted or have compatibility issues, and this often games to crash or lock up. This game has two video files in the Movies directory. I tried playing both of them with mplayer, and they seem to work fine, so I don't think they are corrupted.

I have Ubuntu 20.04. The steps below might not work on other distributions.

Using Wine 6.5 with a 32-bit prefix, and Siege of Avalon Anthology v1.02 (the latest update as of this writing), I got the following error message when I first tried it. (The launch window works, but then it hangs on black screen.)

winegstreamer: error: decodebin0: Your GStreamer installation is missing a plug-in.
winegstreamer: error: decodebin0: gstdecodebin2.c(4678): gst_decode_bin_expose (): /GstBin:bin0/GstDecodeBin:decodebin0:
no suitable plugins found:
Missing decoder: Advanced Streaming Format (ASF) (video/x-ms-asf)

Upon doing some research, I found that 32-bit games sometimes need 32-bit versions of gstreamer plugins that aren't always included in default installations. I installed the following:

gstreamer1.0-plugins-bad:i386 and gstreamer1.0-plugins-ugly:i386

After doing this, the error messages changed as follows:

winegstreamer: error: decodebin0: Your GStreamer installation is missing a plug-in.
winegstreamer: error: decodebin0: gstdecodebin2.c(4678): gst_decode_bin_expose (): /GstBin:bin0/GstDecodeBin:decodebin0:
no suitable plugins found:
Missing decoder: Windows Media Audio 8 (audio/x-wma, wmaversion=(int)2, bitrate=(int)128000, depth=(int)16, rate=(int)44100, channels=(int)2, block_align=(int)743, codec_data=(buffer)00000000010000000000)
Missing decoder: Microsoft MPEG-4 4.3 (video/x-msmpeg, msmpegversion=(int)43, width=(int)1920, height=(int)1080, pixel-aspect-ratio=(fraction)1/1, framerate=(fraction)25/1)

winegstreamer: error: asfdemux0: Internal data stream error.
winegstreamer: error: asfdemux0: gstasfdemux.c(2190): gst_asf_demux_loop (): /GstBin:bin0/GstDecodeBin:decodebin0/GstASFDemux:asfdemux0:

From this, I think it needs some Windows Media codecs or equivalents, and gstreamer doesn't have what it needs. It might need Windows Media Player 8. Winetricks doesn't have that, but it has Windows Media Player 9 (wmp9). I tried installing that, but it didn't fix the problem or change the error messages. It could be worth installing Windows Media Player 8, but I haven't tried that yet.

There are lots of other codec packages floating around the web that sometimes help with older games. Winetricks makes some, but not all, readily available. Some that I've used in the past include K-Lite Codec Pack Basic, LAV Filters, Media Player Codec Pack v4.5.3, and Windows Media Player 9 and 10. There are probably others. It is possible that one of these codec packs will solve the problem, or maybe something else that I'm not aware of will work. I might mess with these eventually if I can find the time or energy, but in case someone else wants to give it a try, this list might be a good starting point.

If anyone else figures this out or makes progress in troubleshooting, please post here - it seems that there are a number of people who would like to play this game on Linux.