Technically you are correct that Belt primarily faced right handed pitching, but given how right handed dominant the top of the Jays lineup was other teams didn't deploy left handed pitching very much against the Jays so this wasn't a huge factor.
Belt appeared in 103 games in 2023. He missed time due to various ailments including separate injured list stints for a hamstring issue (11 days) and back issue (approx. 23 days). He also missed time due to a few stomach bugs and shorter term ailments, to a total of about 40 games or so. The rest of the games he missed were load management and/or lefty starter related. Let's surmise that Belt didn't miss time due to health related issues, and he would have appeared in approximately 140 games for the team if you assume the same ratio of appearances when he was healthy.
In the games he appeared in he averaged 3.92 plate appearances per game, just a half plate appearance per game below regular full time starters for the team such as Bo (4.45 plate appearances per game). In other words you would expect Belt to lose 1 plate appearance every two games he appeared in based on being the strong part of a platoon. Go back to the theoretical 140 game appearance for Belt, and at 3.92 plate appearances per game he would have received 548 plate appearances total vs 683 for Springer and 684 for Vlad, not a dramatic difference for a platoon bat all things considered.
Belt faced left handed pitching in 39 out of his 404 plate appearances, or 9.7% of his total. Compare that to the guys who typically hit around Belt in the lineup like Bo (17.6%) and Vlad (18.1%) and you can easily deduce that Belt was nearly a full time player when he was healthy and available to play. As previously mentioned the Blue Jays top of the lineup was very righty heavy most of the season with the likes of Springer, Bo and Vlad hitting in the top 3-4 spots most of the season so there really weren't many opportunities for opposing managers to deploy left handed relievers against Belt, really limiting the potential impact of his lefty/righty splits.
In 90% of Belt's plate appearances he had the platoon advantage, and he excelled in this split to the tune of a 146 WRC+. Keep in mind that he had a tremendously bad start to the season, and didn't really get his bat going until early May. From May 1 until the end of the season Belt was a 160 WRC+ bat against right handed pitching. So for 5/6 of the season Belt was 60% more effective offensively against right handed pitching in a split where he had the platoon advantage 90% of the time and was typically deployed in 86% of the games when he was healthy and available. In the small amount of plate appearances against left handed pitching during this same 5 month time frame Belt more than held his own as well as he was able to produce a 111 WRC+.