Converting a road bike to a TT bike

Don't do it... the geometry of a road bike is designed with a rearward weight balance, and moving everything forward will cause imbalance. Stick with the road geometry, add shortie (aka ITU) bars and do not change the seat post or stem. You have a road bike, try to make it the best road bike it can be, not a mediocre attempt of a tri bike.

IMHO the most important thing you need are the aerobars, I got some shorties like mentioned above, but I was not comfortable with them at all. Was not able to relax on them as I felt really cramped due to the short distance from the tip of the aerobar to where you elbows/forearms should rest.
Got a pair of normal longer aero bars and got very comfortable. Moved my saddle slightly forwarded and very soon realized I needed a new saddle as the pressure on my groin was very different when I was leaning on the aerobars.
Maybe I was lucky but I found a middle ground where my (new) saddle was still in a fairly normal position so I was comfortable on the drop bar as well as the aero without having to change any stems or posts.

So my advice: aerobars (test the length, are your elbows in the "cup" when your hands grip the front, or do you overshoot by a lot. If the latter, get longer aerobars. And possibly saddle, but that you will figure out after riding with the aerobars.

I added aerobars and moved my saddle forward to shorten the cockpit. This let me be more on top of my elbows in the aero position. This improved my comfort dramatically. Aditionally, a 100 dollar aerocover from wheel buildeer for the rear wheel was a cheap and fast upgrade. There are also carbon wheels from chinese companies that are ridiculously cheap. easy upgrades for performance aerodynamics

i did my IMLOU on a road bike. Anything is possible ;-)

I got a Retul fit that resulted in me adding aerobars, a FF seatpost and a new stem onto my road bike. I was very close to the optimum TT position that way. Some road bike geometry can lend themselves to a decent TT position but it depends.....

I was quite competitive on that road bike in Olympic and HIM races (21 mph ave. in 70.3 races, 23-24 mph in Oly races so it can be done.

For races I roll with clip on aerobars, and a profile design fast forward seatpost on my road bike. Also I'd recommend getting a tri specific saddle. I haven't done a full, but 3 olys and 2 halfs and maybe 10 sprints on the setup, comfortable and fast enough to be competitive.

Others are correct it does compromise handling and balance a bit but by no means does that say you can't or shouldn't do it. Just be aware of it.