It is indeed a bug in the T1 version of GFSArtemisia. This is the part of the fonttable corresponding to Latin smallcaps:

You can see that Ý is listed twice while the first entry should be Ú. This should be reported to the maintainer so it can be fixed.
However, the OTF version from https://ctan.org/tex-archive/fonts/greek/gfs/gfsartemisia/opentype does have ú in smallcaps. So, if you want you can use a rather convoluted workaround to use this character with pdfLaTeX. The idea is to create a pdf file with only this character and set up a mapping in pdfLaTeX from ú to including this pdf, but only for smallcaps (and map to \'u for all other font styles).
Standalone ú smallcaps, compile with XeLaTeX or LuaLaTeX. In the code below this file is referred to as artemisscu.pdf.
\documentclass{standalone}
\usepackage{fontspec}
\setmainfont{GFSArtemisia.otf}
\begin{document}
\textsc{ú}
\end{document}
Mapping, using small caps detection from https://tex.stackexchange.com/a/31660:
\documentclass{scrbook}
\usepackage{gfsartemisia-euler}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[brazil]{babel}
\usepackage{tipa}
\usepackage{newunicodechar}
\usepackage{graphicx}
\makeatletter
\newcommand{\IfSmallCapsTF}{%
\ifx\f@shape\my@test@sc
\expandafter@firstoftwo
\else
\expandafter@secondoftwo
\fi
}
\newcommand{\my@test@sc}{sc}
\makeatother
\newunicodechar{ú}{\IfSmallCapsTF{\raisebox{-0.02Ex}{\includegraphics[width=1.12Ex]{artemisscu}}}{'u}}
\begin{document}
Os números
\scshape Os números
\Huge Os números
\tiny Os números
\normalsize Os n'umeros
Nos capítulos, nas equações...
É mesmo? Então faça com as próprias mãos
Höla e também H"ola. (Exige tipa)
\normalfont
Os números
\end{document}
Note that the size and positioning of the graphic is set in Ex units so it scales with the font size.
Result:

Note that \'u itself is not mapped, so you need the actual ú as input to make it work.
gfsartemisia-euler. That's all. It's meant for Greek. – egreg Mar 11 '23 at 13:30