Talk about losing ugly! Working backwards,
|15.e13 16.f11 did not look any better for white.
|11.f15 12.h16 13.g17 14.g13 also gives black plenty of room.
|7.e18 might have been better, but perhaps K20 was already winning for black.
R19 was strong, setting up for a sort of Medcalf defense with M19. So maybe my R16 was already losing?

Just clicking through this game quickly, I'm probably missing something, but the obvious move not taken was |11.i16 ... What eliminated that from consideration?

How about |11.i16 12.i11 13.j14 14.m11 15.i12 16.j9 for example

Ok, yeah. You're probably already in a losing position no matter what you do by move 10, but at least that line pulls the battle back into open space, and maybe human intuition or luck can rescue the situation. Let me try to fix the line first with |11.t15 12.t18 - does that work? Then the same start on the left side: 13.i16 14.i11 15.j14 16.m11 and then maybe 17.m12... Here's a deep dive; surely TwixtBot would not let this happen: 18.l9 19.n10 20.o8 21.o7 22.n6 23.p9 24.p7 25.r7 26.q9 27.s9 28.r11 29.t11 30.s13 31.u13 32.o15 33.q14 34.p13 35.p12 36.o11 37.o10

Black doesn't have to play R11 in that line. Instead |11.t15 12.t18 13.i16 14.i11 15.j14 16.m11 17.m12 18.l9 19.n10 20.o8 21.o7 22.n6 23.p9 24.p7 25.r7 26.q9 27.s9 28.p11 29.t11 30.o15 or 29.p15 30.t11

Okay so if more of the board is needed for black to win, at least that wouldn't be losing ugly, but it still looks like black was winning from early on.

Indeed.

|5.l13 was an artful move. What was the thinking behind that? I know, early moves can be hard to judge, especially against TwixtBot.

Its reply |6.k20 was surprisingly low - it serves as a catcher for your s18 threat, but looks so weak on the left... so maybe there was a better reply to that? What might have happened if, for example, |7.k18?

|7.k18 might be stronger than I realized. For example 8.l18 9.k22 revives white's threat on the right. So then maybe 10.m15 11.f16, I dunno, this is complicated.

Regarding L13, I felt I had to play centrally because otherwise black could play somethere around J12 with two ways to the right and too close to the left.