@joshieecs I gave this a shot, thanks for the screenshots. I do see the DLC folders and their contents when the DLC are downloaded. Unfortunately, my situation is unchanged.
I uninstalled DAI. I then installed just the base game using EA Desktop, careful to ensure that none of the DLC where checked. I then tested the base game, and it acts as expected - no Trespasser attributes, and old save games not loading due to all the DLC missing. I do note there is a Multiplayer menu item, even though none of the multiplayer DLC are installed, so I guess the base game came with multiplayer and these are just extra modes.
I installed the DLC one at a time, Trespasser last. Testing in between downloads, no change. For example, after installing Jaws of Hakkon it was still listed as a missing DLC when loading an old save game.
I do note that the DragonAgeInquisition.exe has a last modified date of 22/9/2015, and Support/PatchNotes_en.txt tells me the version is 1.12 and is a version later than Trespasser.
I can see installation logs for the DLC, which look successful (well, apart from it thinking I'm running Win8 and not Win10). For example __Installer/DLC/SinglePlayer_DLCBlue/__Installer/InstallLog.txt:
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Install Date: 08/08/2021
14:19:10 Started logging
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14:19:10 Install DLC Location: C:\Program Files\EA Games\Dragon Age Inquisition\
14:19:10 Install Locale: en_US
14:19:10 Initialized installation config.
14:19:10 CommandLine: pdlcinstall -locale en_US -pdlcInstallPath "C:/Program Files/EA Games/Dragon Age Inquisition/" -autologging
14:19:10 EAInstaller version: 4.01.00.00
14:19:10 Original System Version (10.0.19043)
14:19:10 Launching System Version (6.2)
14:19:10 Touchup running under compatibility mode
14:19:10 OS: Microsoft Windows 8 Professional
14:19:10 Data reader initialized.
14:19:10 Data reader config: LOCALE = en_US
14:19:10 Data reader config: PDLC_INSTALL_LOCATION = C:\Program Files\EA Games\Dragon Age Inquisition\
14:19:10 Data reader config: 32BIT = 0
14:19:10 Data reader config: 64BIT = 1
14:19:10 Processing EAIN file 'C:\PROGRA~1\EAGAME~1\DRAGON~1\__INST~1\DLC\SINGLE~3\__INST~1\Touchup.dat'.
14:19:10 Base game installed to: C:\Program Files\EA Games\Dragon Age Inquisition\DragonAgeInquisition.exe
14:19:10 Retrieving base game installed info.
14:19:10 Game (Dragon Age™: Inquisition) with locale (en_US) previously installed at C:\Program Files\EA Games\Dragon Age Inquisition\
14:19:10 (Config)Updating locale to: en_US
14:19:10 (Config)Updating install location to: C:\Program Files\EA Games\Dragon Age Inquisition\
14:19:10 (Config)Studio: BioWare
14:19:10 (Config)Game Name: Dragon Age Inquisition
14:19:10 (Config)Display Game Name: Dragon Age™: Inquisition
14:19:10 (Config)DLC Name: SinglePlayer_DLCBlue
14:19:10 (Config)DLC Display Name: Dragon Age™: Inquisition - Trespasser
14:19:10 The EAIDLC build_guid is 63040a567c084fd7b77d5629062e6972
14:19:10 DLC Install Path: C:\Program Files\EA Games\Dragon Age Inquisition\
14:19:10 DLC Installer Path: C:\Program Files\EA Games\Dragon Age Inquisition\__Installer\DLC\SinglePlayer_DLCBlue\
14:19:10 Start redistributables install phase
14:19:12 End of redistributables install phase
14:19:12 Setting up uninstall data ...
14:19:12 Finished setting up uninstall data.
14:19:12 Setting up registry ...
14:19:12 Installer finished with exit code: 0
14:19:12 Shutting down data reader.
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14:19:12 Stopping install logging
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This all feels like it might be something very simple, such as a config file missing that tells DAI "look for DLC over here"