You are correct in that Redmi Note 13 is using the Samsung ISOCELL HM6. Pros are that it is indeed a larger sensor and has a higher megapixel count. It can supposedly capture slow-motion pictures better. Cons are that the autofocus is slower and less accurate. Samsung, in general, makes more affordable phone camera sensors than Sony, which is the market leader. So I might argue that the ISOCELL HM6 may be cheaper than the LYT600.
Xiaomi/Redmi/Poco are three different lines of phones under the same parent company making decisions on where the value lies. The IMX882/LYT600 is still a pretty capable sensor, and available in phones within last 12 months. I don't think there is anything inherently wrong with choosing LYT600. It's not the best sensor Sony makes, but it's also not a terrible one. One thing to note is that the Samsung HM6 is a 2 year old sensor. If Poco were to use a 2 year old sensor, there would still be someone out there who would accuse Poco of cost-cutting.
I don't know much about Transsion, since Transsion phones are not the most available here. Stuffing a larger sensor isn't the only strategy a phone manufacturer adopts. A bigger sensor isn't necessarily always better. Remember that beyond the flagships, compromises have to be made for every phone part (including software) at every price levels. You cannot simply focus on one single feature and ignore the rest of features on a phone. It's an ecosystem.
Nevertheless, just buy the phone your pocket enables you to do so and is available at the time you are ready to buy. If you want the very best in phone cameras, be prepared to fork out the premium. Will I like a LYT-700/800/900 sensor in Poco X7 Pro? Yes of course, but it's not available on the market and I don't want to pay more than $450 at this point in time. Even at half the price, I am not interested in any Techno or Infinix phone or even Redmi Note 14 as compromises and lack of feature sets in other areas or even support are way too unattractive for me and my needs. However, I am also glad there are consumers buying these other phones which suit their needs. The world is big enough.