Ketchup on hot meat

Even though, yes, we do say that liquid, even if cooked previously is subject a second cooking and therefore you may not heat it up. Putting Ketchup on the potatoes would be permissible since ketchup was once cooked and potatoes bien Kli Rishon is only a stringency.

The Gemara in Shabbat daf 34a :
So it would come out from the Gemara that the decree not to insulate food in something which gives off continual heat (Hatmana) is because maybe you will come to cook. Rashi explains that we are worried ha maybe the food will cool down and you will heat it up on Shabbat thereby cooking.
The Tur learns from here there is cooking on something which has cooled off. But which foods?
The Mishna in Shabbat 145b: Any salted food item that was already placed in hot water, i.e., cooked, before Shabbat, one may soak it in hot water even on Shabbat…Rav Safra said: In the case of the chicken of Rabbi Abba, which for medical reasons was cooked so thoroughly that it completely dissolved. And Rav Safra said: One time I happened to come there and he fed me chicken prepared that way,
The Mishna and Gemara come out that something which is dry food, like chicken you are allowed to heat up on Shabbat if it was cooked before. So which case is the Gemara on Daf 34 discussing? Food which have liquid in them. Heating up liquidy foods is forbidden on Shabbat because it is considered be cooking. The reason the Rishonim give is that the Melacha of Bishul is using fire and heat to change something from non usable to usable, like by piece of pottery, or non-edible to edible. So says the Gemara in the seventh perek .
Something dry changes . For example raw chicken is into edible, but once cooked it changes from and texture it doesn’t revert to being raw when not hot. Liquid on the other hand reverts to what it originally was before being cook. Water gets hot and cools off it the same as it was before. (Although the Ran in Drashot says that water becomes easier to heat once it was cooked. )
There are those Rishonim, the Rashba, Ran and the Maggid Mishna in the Rambam, however who do differentiate like Rashi and they understand the Mishna on 145b is referring to any food. One food is cooked then you are allowed to reheat it.
In the Shulchan Aruch Siman 318:4 the Shulchan Aruch rules stringently like Rashi reheating cold liquid is coking. The Rema in 318:15 quotes the opinion that reheating is not cooking. The Rema compromises the opinions says that we should be stringent if the liquid is completely cool. If it is still warm then you may reheat it.
So Ketchup or tabasco are liquids so according to the Shulchan Aruch there is cooking by heating them up and according to the Rema if they were hot already fine but if they are cold there a problem of Bishul.
That is when you actually heat up the ketchup in pot, however squirting some on hot Cholent or chicken is a different issue. There is a Halacha in Shulchan Aruch that the is no such thing as ‘cooking’ in Kli Sheni. The Kli Sheini is a plate or a bowl which you poured food into from a Kli Rishon, a pot which was on the fire. The Magen Avraham (318:45) quotes the Maharshal in Hilchot Taarovet in Yoreh Deah says that a Davar Gush, a big chunk of food, retains its heat even after it is placed into Kli Sheni and it still cooks. The Magen Avraham ,and the Mishna Berura quotes him, on Shabbat we are stringent like this opinion and we have to be careful with the potatoes.
R Moshe Feinstein Orach Chaim 4:74 writes that putting ketchup on a Davar Gush is permitted. Since the Rema himself really holds like the opinions that there is no Bishul by reheating, he is just stringent to be sure it is still hot, we do not combine two stringencies together and you may put the Ketchup on the potato or meat since it is only a Davar Gush.
The Sephardim who are stringent like the Shulchan Aruch and forbid reheating liquid would also be lenient in this case. Since the Shulchan Aruch does not have a concept of Davar Gush at all, then there is no reason why not to put ketchup on.
The one thing you must determine is if Tabasco or any of the condiments were actually cooked in processing. If they were pasteurized it would be considered Bishul. If not then it would be forbidden to put it on a Davar Gush.