My understanding is the following:
Time to Interactive (TTI) is when the website is visually usable and engaging. For example, when a user can click around on the UI and the website is functional. Ideally, we want all experiences to get interactive as soon as possible. Examples of websites with poor TTI are websites where a user can be actively engaged with the UI for a good amount of time before anything actually happens. Poor TTI is caused by too much (main thread) JavaScript which adversely causes delays for interactivity for visible UI elements. An example, of this is here. This is an especially important metric to consider for the mobile space since everyone doesn't have a nice phone (so it will take longer to parse the JavaScript needed to load a site) as well as the variance that occurs due to different network speeds: i.e. WI-FI, 3G, 4G
domInteractive however is when a page's primary content is visible and meaningful paints have occurred. At this stage a user can visually see the webpage and the corresponding UI elements that represent the site's DOM.
First Input Delay (FID) is the measurement of how long it took to respond to a user event. For example, how long did it take for a button's event handler to take over and respond once the user clicked the button.
As far as I know FID and TTI are experimental metrics right now so they probably wouldn't be baked into Google Analytics by default. As for your question: "Am I better off tracking TTI on my users if I'm concerned about input delays affecting conversion, or am I fine to stick with domInteractive?" You actually want to track FID if you're concerned with input delays affecting conversion. TTI is still a very useful metric to track since it measures when your site as a whole is interactive and both TTI and FID will provide more value than domInteractive.
If you're still interested check out this explanation on the Cost of JavaScript by Addy Osmani. He does a beautiful job explaining the performance issues we are facing with JavaScript as well as talking about TTI and FID.
Cheers