An Nvidia GPU should be able to accelerate nearly any AI workload as long as there is enough video memory for it. It should be fairly easy to pass through if you use Proxmox as the hypervisor. However just having the GPU available will not help with BI's transcoding. You can specify to
Blue Iris to use the GPU for hardware accelerated decoding and/or encoding purposes (these are configured in different places in BI) but it will not make a tremendous difference in CPU usage, and it will most likely raise your system's power consumption instead of reducing it. Just adding the GPU will raise power consumption significantly though even if you aren't using it for anything yet.
For storage, I'm not sure what you mean by "storing live streams and triggered content". BI lets you record each camera continuously OR event-triggered, but not both to different places unless you clone the camera instances. The rule of thumb for best storage performance and reliability is to not move clips when the drive is full, just delete them. If you have multiple hard drives, split the load by configuring some cameras to record to each of the drives and just have each drive configured to delete clips when full.
By having Blue Iris move clips between drives, both drives get the full load of having all clips written onto them, but you also double the workload of the first drive because now it must read every clip file completely one extra time. For a properly functioning hard drive this shouldn't cause much wear and tear but it can slow down the access time when you want to read clips that are on the first hard drive. This configuration also increases the complexity of Blue Iris's clip management duties, and many of us who have been using Blue Iris for a long time have encountered issues before with Blue Iris failing to move files off a full disk because of some bug.
SSDs perform great for storing Blue Iris video and will make access time / seek time better especially when playing recordings for a group of cameras via the Timeline. This is one case where it is justifiable to record directly to the SSD and when full move the clips to a hard drive for longer term storage.
Just make sure you check the SSD's endurance specification and avoid buying one with a low amount of endurance. Endurance is usually labeled "TBW" meaning "terabytes written". Doubling the drive capacity usually doubles the endurance. The average 4 TB SSD should have around 2400 TBW for its endurance spec, meaning the manufacturer will warranty the drive for up to 2400 terabytes of total writes (or until the regular warranty period expires, whichever happens first). It isn't a hard limit for the amount of data you can write to the SSD before it fails, but it is the best indicator we have of how long it should last. So If you buy a 1 TB SSD you can expect it to last about a quarter as long as a 4 TB SSD would, under the same video recording load.
Hard drives advertised for specific duties (e.g. NAS or NVR/surveillance) are kind of an unknown value. Hard drive manufacturers tend to be unspecific about the exact benefits. Like, we don't know if they used higher quality materials, better cooling technology, or maybe the firmware is coded to prevent long delays due to trying to read or write a bad sector. Or maybe it is just a different sticker on the drive and a different device identifier written into its firmware. We just don't know. So people just buy them based on the belief it will be slightly more reliable in the long term. I don't worry about it for drives where I'm going to be recording only on event triggers. But for stuff where I'll record continuously, I do prefer to buy a "surveillance" hard drive for the peace of mind.
BI 6 will be coming out soon but I get the feeling that won't be a hugely significant update. BI doesn't operate on a "buy the new major version upgrade" pricing model anymore. It is just a "pay for the next year of updates" model, so there's not much incentive to hold back new features for version 6. Heck the version 6 color scheme has already been making its way into version 5 in the last few patches.
There have been way too many changes to summarize between 5.6.5 and 5.9.9.90 which we're on now. Nothing huge that I can think of. Maybe AI integration is better but I don't use AI so I wouldn't really know. If you reinstall on new hardware or want to get started using AI with it, then I would definitely recommend renewing your support plan and installing the latest version. But otherwise if 5.6.5 works well for you, then it wouldn't hurt to stick with it.