Astounded to find the HDD in my laptop is 10 years old. It's a Seagate Momentus 7200 750 GB 7200RPM SATA 3Gb/s 16 MB Cache 2.5 Inch Internal Notebook Hard Drive -Bare Drive ST9750420AS

Smart Data Indicates:
Read Error Rate Pre-Fail OK
Spinup Time Pre-Fail OK
Reallocated Sector Count Pre-Fail OK
Seek Error Rate Pre-Fail OK
Spinup Retry Count Pre-Fail OK

Everything Else is Old-Age OK
/home is 689 GB containing 192.231 GB (Thats after a lot of house cleaning)

I plan on backing up /home to a new Western Digital Black external HDD tonight. I use Timeshift to backup / to a thumb drive.

I will continue running the Seagate to see how long it will last.

How do I interpret the fields Attribute, Value, Normalized, Threshold, Worst.
Will Smart Data - Self Tests issue a notice of likely failure?

It helps to see the raw data especially the critical parameters. See wikipedia
https://en.wikipedia.org/wiki/S.M.A.R.T.

Apart from POH (Power On Hours) a lot of these are relative - as in the value that a given model, manufacturer, etc considers to be 'acceptable' or 'unacceptable' varies from device to device (so it isn't just enough to say 'all should be 0 everywhere' or 'all should be 100 everywhere' - that doesn't make sense). If it's passing 'OK' it isn't tripping any of its pre-failure or failure sensors, so its OK. Standard advice to maintain backups always applies - the failure of a single storage device should be weighed as time-to-recover not 'will all of my data be gone forever in a flash.'

I highly recommend gsmartcontrol for this - because of the detailed tooltips you get.
But I also use "normal" smartctl for launching tests etc.
Some notes.