How do I recover lost photo albums on iMac?

We can't see your machine, much less read your mind. We rely on you to give us enough information so that we can understand your issue if we are to help. We need a full description of the issue, information on what devices or machines you're referring to, the operating system (and version of it) currently on the machine. What you expect to happen, and where it fails. Err on giving too much information rather than too little.

With all that you have offered here - and what does your Phone have to do with it? - the best I can suggest is that you restore from your back up.

Sorry lucylobster, in your original question you wrote "iPhoto" and mentioned albums created since 2005, and that was a bit confusing, since iPhoto has been deprecated by Apple and does no longer run on any Mac with macOS 10.15 Catalina or later.

So your "albums created since 2005" have been created with iPhoto, but you are now using Photos 9 on Sonoma? Are the old iPhoto Libraries missing, from the years before you switched from iPhoto to Photos? Or are albums in your Photos Library are no longer shown - the albums that used to be shown in a folder iPhoto Events?

If only the albums are missing, but not the photos, I recommend to recreate the yearly albums as smart albums in Photos to make it easier to find the old photos:

For example - to recreate your early album for the year 2005:

• Create a smart album with "File > New smart album.
• Set the rule to "Date captured is in the Range " and specify a range of one year like this: