Ok, so I've decided to do my guesses for the Senate elections until the last properly contested elections in 2046 because why not. I will also be excluding any special elections:
2016:Dems gain: IL, NH (as OTL)
D+2 (52R-48D)
2018:Republicans gain: MT, ND, MO, IN, OH, WV, FL, NJ, WI
R+9 (61R-39D)
2020:Dems gain: CO
D+1 (60R-40D)
2022:Republicans gain: NH, NV
R+2 (62R-38D)
2024:Dems gain: NJ, NV
Republicans gain: ME, MI
No net change (62R-38D)
2026:Dems gain: AZ, TX, GA, NC, ME
D+5 (57R-43D)
2028:Dems gain: NV, AZ, GA, FL
D+4 (53R-47D)
2030:Republicans gain: MN, PA
R+2 (55R-45D)
2032:*
Republicans gain: NH, ME, TX, NC
R+4 (59R-41D)
2034:Dems gain PA
D+1 (58R-42D)
2036:Dems gain AZ, TX
D+2 (56R-44D)
2038:Dems gain TX, NC
D+2 (54R-46D)
2040:*
Dems gain: AK, KS, WI, SC, NC, NH
D+6 (52D-48R)
2042:*
Republicans gain NV, AZ, TX, VT, RI
R+5 (53R-48D)
2044:*
LBS gain MN, MI
LBS+2 (55LBS-45D)
2046:*
LBS gain NH, PA, WI, NC, GA, FL, KS, AK
Dems gain Guam (x2), NMI (x2)
Net LBS+4 (63LBS-41D)
In fairness I think most of these results should be more "mixed" (only election with both D and R pickups is the 2024 realining election; excluding the 2046 midterms) but they still give us an idea. And after this, my mini-review of my guesses.
*1: Given Dems are quite overextended in 2032 as well as Hawley's convincing victory; it is kind of surprising Republicans don't win more seats, you could easily go all the way to R+8. I went with a mix of trends (NH, ME) and old GOP states coming home (TX, NC) but you could do all one or the other.
*2: Getting Dems to win the required Senate majority in 2040 requires several unorthodox pickups. AK, KS and NC are easy pickups given Ramirez-Rosa carries them, but the next 3 are quite hard to get unless you assume Dems hold states like WI and NH in 2028 and 2034. If you do, it gets easier though in any case you still fall 1 state short I think. I decided to give those 2 back to the Dems, as well as SC since that seemed like the most plausible pickup. Or you could also make up 1-2 special elections or flip other states like say, UT or ID
*3: Here you run into the same problem but in reverse. Unless you assume Dems hold to the Midwestern seats while the GOP holds the Southwest up until 2040; it is very hard to get the required 5 pickups. I went with giving Republicans 3 of their former competitive states (NV, AZ, TX) as well as 2 states that probably trended to them for quite a while at this point (VT, RI)
*4: Given the election was mostly rigged I am surprised President Gallagher didn't give himself a bigger Senate majority
*5: Decided to go with the unorthodox decision of giving the Dems the Senators for Guam and the Marianas. President Gallagher is very disappointed at their treason
Anyways that way the Liberators can sweep the mainland US seats.
I guess I went too far into the trends direction in a way I suppose