Fitness for what?
Chris Hoy or Chris Froome?
Usian Bolt or Eliud Kipchoge?
Fitness is defined by your own goals and achievements which can be informed by TSS, CTL and other cycling training metrics and concepts but aren’t entirely defined by them. @Landis rightly lists several ways in which ‘fitness’ could be measured based on different cycling goals.
You say you are training for a HIM so presumably your bike fitness in this period will be defined by the power you can sustain for the time the bike leg will take.
To take a hypothetical example which you yourself allude to in your last post - you take a short test and find your FTP is 250W but know you can hold 200W for the duration that your HIM. After some training over the HIM distance you can now hold 210W for the duration but when you repeat the short test to determine your FTP (which all the other metrics are based off) because you’ve only been training over the HIM distance that number goes down slightly as you haven’t trained it. Are you fitter? If you measure based on the FTP number you’re less fit. If you base it on what you are actually training for you are objectively fitter.
This scenario is possibly unlikely as training based on a sound plan will likely see improvements at many durations even if they aren’t the specific focus of the training itself but illustrates the difficulty of relying on the algorithms of CTL and TSS. They are based on the somewhat nebulous concept of ‘FTP’ - a metric which can mean the power you can hold for somewhere between 40 minutes to over an hour which we as cyclists distill into a single, precise number based on a one test, at one moment in time often over a different duration than the one it’s supposed to represent.
One way of achieving this is to track power at different durations over time. As you’re training for a HIM you could create a chart (I use Golden Cheetah for analysis but there are many others and you can easily create a simple spreadsheet) tracking 30m, 1h, 90m, 2hr and 3hr power. Use a trendline and if the numbers that you are particularly concerned with trend upwards you are objectively getting fitter for the event you are training for.
Chances are if you follow one of TR’s plans which are based on progressive overload and increasing specificity toward your goal event this should happen anyway. If you regularly see TrainerRoad PR’s appear on some of the key workouts while following a plan you’ll be on the right track.