A naive approach would be to define a command to hardcode the text for the middlehead and lasthead. With the command \SetMidLastCaption, you can place any text you like in the "continued captions".
Obviously, it would be much better to define a new key, e.g. mid-caption as you suggested. However, I am not that familiar with expl3, maybe someone else can help.
Found a solution, see edit below.
\documentclass{article}
% "margin = 54mm" is used to control the page break for the MWE.
\usepackage[a4paper, margin = 54mm, landscape]{geometry}
\usepackage{tabularray}
\UseTblrLibrary{booktabs}
\ExplSyntaxOn
\NewDocumentCommand { \SetMidLastCaption }{ m }{
\DefTblrTemplate{ middlehead, lasthead }{ default }
{
\centering
#1
\par
}
}
\ExplSyntaxOff
% Use the following command to reset the captions to normal behaviour
%\SetTblrTemplate{middlehead,lasthead}{normal}
\begin{document}
\SetMidLastCaption{Other Captions}
\begin{longtblr}[
caption = {First Caption},
% mid-caption = {Other Captions}, % <-- Pseudo Code :)
entry = {LoT Caption},
label = {tab:label};
]{
colspec = {t{0.20\linewidth}t{0.20\linewidth}t{0.20\linewidth}},
rowhead = 1,
row{1} = {font=\bfseries},
}
\toprule
A & B & C \\
\toprule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\\midrule
a & b & c\\
\bottomrule
\end{longtblr}
\end{document}

Edit: Defintion of new key midlast-caption
The following code defines the key midlast-caption as an outer key (used in the optional argument) for tblr. The assignment should be local, meaning if you do not provide the key the captions should use the normal template. If you use midlast-caption = {Other Captions} in the optional argument, the result will be the same as in my first example.
\ExplSyntaxOn
\clist_gput_left:Nn \g__tblr_table_known_keys_clist { midlast-caption }
\keys_define:nn { tblr-outer } { midlast-caption .code:n = \__tblr_set_midlast_caption:n { #1 } }
\cs_new_protected:Npn \__tblr_set_midlast_caption:n #1 {
\DefTblrTemplate{ middlehead, lasthead }{ default }
{
\centering
#1
\par
}
}
\ExplSyntaxOff
Disclaimer I am a complete novice to expl3. Therefore this code might be very bad, use it with caution. I am thankfull for everyone who improves this code.
lastheadnotmiddlehead. – marv Feb 21 '22 at 21:27