Does Buddhist Literature mention any of the former Buddhas taking birth in Kikata-Pradesa (Modern day Gaya)?

There’s a new theory, which I saw many Vaiṣṇava groups propagating, of the 2 buddhas: Viṣṇu incarnate Ādi Buddha and the other being Śākyamuni of Buddhism, as two seperate personalities, based on the differences in Buddha stories from the Vaiṣṇava texts and Śākyamuni’s story in Buddhist texts. I have briefly talked about it in the addendum to this answer as well. They cite the details mentioned in the Bhāgvata Puruāṇa to claim that Viṣṇu-incarnate Buddha was a different person born centuries before the Gautama Buddha, gave teachings of compassion and leaving animal slaughter, then centuries later Siddhārtha came to bodh gaya, gained enlightenment there as the place had increased spiritual potency. To Quote from this article - > tatah kalau sampravritte sammohaya sura-dvisham > buddho namnanjana-sutah kikateshu bhavishyati > (srimad-bhagavatam 1.3.24) > > “Thereafter, in the twenty-first manvantara at the beginning of > Kali-yuga, the Lord will appear as **Lord Buddha, the son of Anjana, > in Kikata Pradesa (the province of present day Gaya-Bihar)**, just for the purpose > of deluding those who are envious of the faithful demigods.” As anyone can see that the stated birth place does not coincide with the Birth place of the historical Gautama Buddha. To supposedly reconcile this apparent contradiction, they cite the theory that the Vishnu incarnate buddha was a different person from Gautama buddha for which they cite the following proof- > Thus, Sugata Buddha and Sunyavadi (Sakyasimha) Buddha are not the same > person. Further evidence is found in Mr. H.T.Colebrooke’s Amarakosha, > published at Ramapura in 1807. It is written in Chapter 21, Page 178 > of Lalitavistara-grantha that Gautama Buddha performed penances at the > same place as the previous Buddha (Vishnu-avatara Buddha). Maybe it is > for this reason that in later ages he and Lord Buddha are considered > as being one: > > esha dharanimunde purvabuddhasanasthah > samartha dhanurgrihitva sunya nairatmavanaih > klesaripum nihatva drishtijalanca bhitva-siva > virajamsokam prapsyate bodhimagryam What's more to support this notion, they cite even a Buddhist text named Lankavatara-sutra - > There is an authentic Buddhist book, Lankavatara-sutra, in which > Ravana, the king of Lanka, prays to Jina’s son, the ancient Lord > Buddha, and to all the Buddhas and Buddhas’ sons who would appear in > the future, via this eulogy (stava): > > atha ravano lankadhipatih gathagiten anugayati sma > lankavatarasutram vaih purvabuddhanuvarnitam > smarami purvakaih buddhairjinaputra-puraskritaih > putrametannigadyate bhagavanapi bhashatam > bhavishyantyanapate kale buddha buddhasutasca ye > > Therefore, this source leaves no doubt that the ancient avatara-Buddha > and the modern Gautama Buddha are not the same person. Questions - 1. As I saw from the Answers of this question , there is indeed a conception of many Buddhas in the Buddhist literature. Does any of the buddhist literature mention any account one of the former buddhas taking birth in Present Day Gaya (Kikata-pradesa)? 2. Since it is Gaya alone where Gautama Buddha attained enlightenment, Does Gautama buddha mention any of the former buddhas taking birth in that place in any of his discourses? As the Buddha was omniscient, he would have certainly known about the former buddhas and if any of them had actually taken birth in kikata pradesa (aka present day Gaya).