See M-W: welcome {adjective} {3}: 'willingly [gladly] permitted or admitted'. Compare 'We were happy to oblige' / 'You are free to apply' (not 'freed to apply'). //// There are a disturbingly large number of examples of 'welcomed to apply' on the internet.
– Edwin AshworthMar 21 '21 at 14:24
In this context, welcome has the sense of permission while welcomed has that of hugs as an inducement to apply.
– LawrenceMar 21 '21 at 16:05
@EdwinAshworth Perhaps posts saying "Foreigners are welcomed to apply" are placed by foreigners to English-speaking countries
– BoldBenMar 22 '21 at 00:02