Here is an update on this - posted separately so that @wrybread sees it, too. 
Since I hadn't actually disposed of my SD49225T-HN - just put it into storage - and was curious, I decided to dig it out again.
First, I need to correct my earlier statement claiming it already had the 2024 firmware version installed. I had assumed I had installed that update at some point, but it actually still had the 2021 firmware on it.
So, I tried applying the update using the 2026 firmware version I had downloaded earlier from the German Dahua website (DH_SD-Mao-Rhea_MultiLang_PN_Stream3_IVS_V2.800.0000000.8.R.260903), and - lo and behold - it installed without any issues.
Incidentally, I performed the installation using the Waterfox browser. 
I’m not yet sure if I’ll give this old SD49225T-HN another chance after six years of service,
but I’m going to leave it connected and sitting on my desk for a few days. We’ll see if that "rogue PTZ behavior" rears its head again.
Edit:
Perhaps this DHCC-SA-202606-001 is the reason for those "2026" updates from August and September:
www.dahuasecurity.com
Even though the SD49225T-HN model does not appear here:
In any case, I was unable to find any other current and relevant security advisories from Dahua from the same timeframe.
Since I hadn't actually disposed of my SD49225T-HN - just put it into storage - and was curious, I decided to dig it out again.
First, I need to correct my earlier statement claiming it already had the 2024 firmware version installed. I had assumed I had installed that update at some point, but it actually still had the 2021 firmware on it.
So, I tried applying the update using the 2026 firmware version I had downloaded earlier from the German Dahua website (DH_SD-Mao-Rhea_MultiLang_PN_Stream3_IVS_V2.800.0000000.8.R.260903), and - lo and behold - it installed without any issues.
Incidentally, I performed the installation using the Waterfox browser. I’m not yet sure if I’ll give this old SD49225T-HN another chance after six years of service,
but I’m going to leave it connected and sitting on my desk for a few days. We’ll see if that "rogue PTZ behavior" rears its head again.
Edit:
Perhaps this DHCC-SA-202606-001 is the reason for those "2026" updates from August and September:
DHCC-SA-202606-001: Security Advisory – Vulnerabilities found in some Dahua products
CVE-2026-29114, CVE-2026-29115, CVE-2026-29116
Even though the SD49225T-HN model does not appear here:
In any case, I was unable to find any other current and relevant security advisories from Dahua from the same timeframe.
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