I moved the Mods folder to the desktop and the game worked fine. Once I've put it back, there was the same issue. Now I reduced the number of mods to 60. What I left are the following:
00|altea127's lingerie for little girl
01|Angel of Fire
02|Beauty of the Orient
03|Chaotic Elements - Water_ziggy28TSR
04|Chaotic Elements Fire_ziggy28TSR
05|Dragon Attack
06|ESkin-nATURAL+Default-F
07|ESkin-Natural+Light
08|F-P_1985_Toyota_Sprinter_Trueno-AE86_TS3
09|F-P_2018-Honda-Civic-Type-R_TS3
10|Fairies_byRirann@TSR
11|Fairy painting 3
12|Fairy Wings_ziggy28TSR
13|Fantasy Dream Eyeshadow
14|fantasy II
15|Fantasy Picture 1
16|Fantasy Picture 2
17|Fantasy Style Anime Eyes
18|Fantasy.disabled
19|Flower Fairy_marcorse
20|Frozen Blossoms_ziggy28TSR
21|Futuristic Painting #1 by DP
22|Futuristic Painting #2 by DP
23|Futuristic Painting #3 by DP
24|Futuristic Painting #4 by DP
25|gemini_ziggy28
26|GirlsSwimwear
27|Juliana_AdidasSportPants_Child
28|Juliana_AdidasSportShorts_Child
29|Juliana_AdidasSportTop_Child
30|Magic Garden_marcorse
31|Moonlight Unicorn
32|Nightcrawler_AF_Hair_Moonlight
33|NoBuildSparkles
34|nointromaxis
35|PaintingGirlFantacy
36|Painting_Fantasygodess
37|PSpsnaturalA
38|PSpsnaturalND
39|Red Dragon By Dragoncat
40|S3 Child Onesie Mh75
41|sebrof77 - Chio v05-17-1750
42|sebrof77 - Song of Clouds v05-24-1402
43|sebrof77 - The Keeper v05-17-1750
44|sebrof77 - Too Cold to Snow v02-04-1035
45|sebrof77 - Whisper v05-17-1750
46|Sims3_Lemonleaf_skin A2.5 Non Default
47|Sims3_Lemonleaf_skin B2.5 Non Default
48|Snowfall_marcorse
49|Sonata77 child girl 13
50|StargirlHair_001
51|Swimwear for girls
52|The Colour of Dreams_marcorse
53|The Red Tour - Love Story Dress
54|There Be Dragons_marcorse
55|TS_Modern Art II
56|Winter Roadway_marcorse
57|Winter Wonderland By Dragoncat
58|ziggy28_libra
59|[PS] Dragon Blood Eyeshadow
2 cars, couple of clothes, skins & makeups. The rest are paintings.
I tested the game with a new Documents\Electronic Arts\The Sims 3 folder and the results were the same; it worked without the mods but lagged with the mods. There's also lag if the mods are in place but the 'Run without CC' option is checked in the launcher. I also tested the game with only the nobuildsparkles and the NoIntroMaxis mods left and it also works fine. Now I'll test it with only the above listed mods and update this comment to include the results.
Edit: the game runs fine with only these mods. Now, I'll put back everything else (except for Story Progression) and see what happens.