It was my understanding that simply muxing srt subs to mkv retains them as text objects and are thus dependent in their appearance and presentation on the renderer used in the player and its default handling (ie font style, colour, size and positioning). I don't think muxers usually change or convert text objects: this requires other software.
External srt subs are useful in that they can often be played along with an mkv, although only a single instance is allowed which must be named the same as the mkv file. Being external they can be readily edited for changes. Muxing srt into an mkv file allows multiple subtitles to be incorporated and any forced subtitle identified, but it is up to the player to permit selection and the honouring of forced attributes. Editing of muxed srt subs requires demuxing and remuxing: a reasonably simple process, but more complex than simply using external subs.
If one wants consistent subtitle presentation regardless of renderer and a specific font style, colour, size and position, then graphic based subtitles are required (specifically PGS for Bluray standard). These can not be as readily edited as srt subs and are therefore desirable once the subtitles have been finalised and require no more changes. I understand EasySup and GoSup are freeware for converting srt subs to PGS.
BDsup2sub is freeware that permits modifying characteristics of graphic subtitles (scaling, positioning, palette, etc) but can not edit the text itself.
I am unsure whether Harmy intends to use a specific font style, size, colour and positioning for subtitles, but if so then PGS subtitles are the solution for the Bluray. Whether these PGS subtitles are included in the mkv is a different matter, however it is quite easy to mux standalone PGS or srt files into an mkv with mkvmerge and so these files could be supplied individually and independently of the mkv.
An mkv makes a very good pre-container for a Bluray since software such as ClownBD can convert mkv to Bluray structure quite easily, plus the mkv is effectively presented as the final Bluray (apart from menus) in players which support it.