OK, I ended up answering my own question 
Here are the steps I followed in case anyone ever ends up in this situation. As I had an existing older backup (z9d47fe2.tar), I extracted the tar file contents into my local desktop. There were a bunch of tgz (tar.gz) files within the backup and a json file as well. Some of the tgz files were devoid of content because I didn’t have those add-ons enabled - media, share, ssl, etc. I checked their contents using gunzip -c <file.tar.gz> | tar tvf -. The backup.json file had some info related to the backup itself - name, size - and there was a section named “folders” that listed the above addons with empty tgz files.
Next, I copied my current HA config directory contents into a new directory called data and then made a new homeassistant.tar.gz file from it. Finally, I copied this new homeassistant.tar.gz file into my desktop where I had extracted the previous backup’s contents. Now, I removed the empty tgz files which then left me with some Samba, SSH, etc. tgzs and the homeassistant.tar.gz file. I modified backup.json and removed the deleted tgzs’ entries from the folders section in backup.json, leaving it blank. Lastly, I gave my backup a new name (z9d47fff) and modified the size by dividing the new size 34844156 with (1024 * 1024) to get the size in MB which gave me 33.2299 which rounded off to 2 decimals gave me 33.23.
Once this was all done, I created a new tar file (z9d47fff.tar) from the current contents and gave it the name I had entered in backup.json. I uploaded that to HA on my new SSD that had been upgraded to HAOS 9.33 and was successfully able to restore the backup.
> tar tvf z9d47fe2.tar
drwx------ 0 root root 0 Oct 07 2021 ./
-rw-r--r-- 0 root root 177 Oct 07 2021 ./addons_local.tar.gz
-rw------- 0 root root 766 Oct 07 2021 ./backup.json
-rw-r--r-- 0 root root 1334 Oct 07 2021 ./core_configurator.tar.gz
-rw-r--r-- 0 root root 1419 Oct 07 2021 ./core_samba.tar.gz
-rw-r--r-- 0 root root 8203 Oct 07 2021 ./core_ssh.tar.gz
-rw-r--r-- 0 root root 8712309 Oct 07 2021 ./homeassistant.tar.gz
-rw-r--r-- 0 root root 169 Oct 07 2021 ./media.tar.gz
-rw-r--r-- 0 root root 169 Oct 07 2021 ./share.tar.gz
-rw-r--r-- 0 root root 168 Oct 07 2021 ./ssl.tar.gz
> mkdir ha_restore
> cd ha_restore
> tar xvf ../z9d47fe2.tar
x ./
x ./addons_local.tar.gz
x ./backup.json
x ./core_configurator.tar.gz
x ./core_samba.tar.gz
x ./core_ssh.tar.gz
x ./homeassistant.tar.gz
x ./media.tar.gz
x ./share.tar.gz
x ./ssl.tar.gz
> ls -ltr
-rw-r--r-- 1 root root 1419 Oct 07 2021 core_samba.tar.gz
-rw-r--r-- 1 root root 1334 Oct 07 2021 core_configurator.tar.gz
-rw-r--r-- 1 root root 8203 Oct 07 2021 core_ssh.tar.gz
-rw-r--r-- 1 root root 8712309 Oct 07 2021 homeassistant.tar.gz
-rw-r--r-- 1 root root 169 Oct 07 2021 share.tar.gz
-rw-r--r-- 1 root root 177 Oct 07 2021 addons_local.tar.gz
-rw-r--r-- 1 root root 168 Oct 07 2021 ssl.tar.gz
-rw-r--r-- 1 root root 169 Oct 07 2021 media.tar.gz
-rw------- 1 root root 766 Oct 07 2021 backup.json
> cat backup.json
{
"version": 2,
"slug": "z9d47fe2", <<<<<<< Rename to new file name of backup
"name": "HA_100721", <<<<<<< Rename to new name of backup
"date": "2021-10-07T04:25:13.092266+00:00",
"type": "full",
"crypto": null,
"folders": [
"share", <<<<<<<<< Removed these 4 lines
"addons/local",
"ssl",
"media"
],
<<SNIP>>
"homeassistant": {
"version": "2021.5.1",
"size": 8.31 <<<<<<<< Calculate new size
}
}
> rm share.tar.gz ssl.tar.gz media.tar.gz addons_local.tar.gz
> cp /tmp/homeassistant.tar.gz .
> ls -ltr homeassistant.tar.gz
-rw-r--r-- 1 root root 34844156 Nov 23 2022 homeassistant.tar.gz
> vi backup.json
> cat backup.json
{
"version": 2,
"slug": "z9d47fff",
"name": "Post_SSD_UPG",
"date": "2021-10-07T04:25:13.092266+00:00",
"type": "full",
"crypto": null,
"folders": [
],
<<SNIP>>
"homeassistant": {
"version": "2021.5.1",
"size": 33.23
}
}
> ls -ltr
-rw-r--r-- 1 root root 1419 Oct 07 2021 core_samba.tar.gz
-rw-r--r-- 1 root root 1334 Oct 07 2021 core_configurator.tar.gz
-rw-r--r-- 1 root root 8203 Oct 07 2021 core_ssh.tar.gz
-rw-r--r-- 1 root root 34844156 Nov 23 2022 homeassistant.tar.gz
-rw------- 1 root root 715 Nov 24 19:40 backup.json
> tar cvf ../z9d47fff.tar ./core_samba.tar.gz ./core_configurator.tar.gz ./core_ssh.tar.gz ./homeassistant.tar.gz ./backup.json
a ./core_samba.tar.gz
a ./core_configurator.tar.gz
a ./core_ssh.tar.gz
a ./homeassistant.tar.gz
a ./backup.json
> ls -ltr ../z9d47fff.tar
-rw-r--r-- 1 root root 34860544 Nov 24 19:54 ../z9d47fff.tar