(Question is not that long, just a lots of images and code examples)
I'm trying to merge two independents tikzpictures like these:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,math}
\usetikzlibrary{shapes.misc}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\pgfplotsset{my style/.append style={clip = false, axis lines* = middle, axis equal, xtick = \empty, ytick = \empty, xmin=-1, ymin=-1}}
\begin{document}
% First picture
\begin{tikzpicture}
\begin{axis}[my style]
\addplot [green, fill, fill opacity=0.2, domain=0:360, samples=40] ({1+cos(x)0.8},{1+sin(x)0.8});
\end{axis}
\end{tikzpicture}
%Second picture
\begin{tikzpicture}
\begin{axis}[my style]
\addplot [red] coordinates {(1,1)(0,0)};
\end{axis}
\end{tikzpicture}
\end{document}
Preserving the original coordinates from each one. And I'd like to be able to merge both obtaining the same picture as if I'd do:
\begin{tikzpicture}
\begin{axis}[my style]
\addplot [green, fill, fill opacity=0.2, domain=0:360, samples=40] ({1+cos(x)*0.8},{1+sin(x)*0.8});
\addplot [red] coordinates {(1,1)(0,0)};
\end{axis}
\end{tikzpicture}
(Please don't answer "Then, just do that". I want to obtain that result from two independents tikzpictures)
So, the original pictures are:
And the expected result is:

I've read:
Combining two tikz plots together
But I think the only thing that fits my problem is this comment https://tex.stackexchange.com/a/96900/222098. I've tried that solution this way:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,math}
\usetikzlibrary{shapes.misc}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\pgfplotsset{my style/.append style={clip = false, axis lines* = middle, axis equal, xtick = \empty, ytick = \empty, xmin=-1, ymin=-1}}
\begin{document}
\begin{tikzpicture}
\node [] at (0,0){
\begin{tikzpicture}
\begin{axis}[my style]
\addplot [green, fill, fill opacity=0.2, domain=0:360, samples=40] ({1+cos(x)0.8},{1+sin(x)0.8});
\end{axis}
\end{tikzpicture}
};
\node [] at (0,0){
\begin{tikzpicture}
\begin{axis}[my style]
\addplot [red] coordinates {(1,1)(0,0)};
\end{axis}
\end{tikzpicture}
};
\end{tikzpicture}
\end{document}
And the result is:
But that solution doesn't preserve the original coordinates (and I'd prefer not to have to do it manually). One of the pictures seems to have not its correct coordinate system scale in the new merged one.

tikzpictures: https://tex.stackexchange.com/a/46792. I don't know how one can do this, or if it's even possible, but what kind of limitations are there? Can one edit the code of thetikzpictures in any way? (If it were me, I'd comment out\end{axis}\end{tikzpicture}from the first, and\begin{tikzpicture}\begin{axis}[..]from the second, but that's not an option I take it.) – Torbjørn T. Aug 25 '20 at 17:11scopeonly works inside atikzpicture, it's purpose is to add the same options to a subset of the paths in the diagram. – Torbjørn T. Aug 25 '20 at 17:25tikzpicture[remember picture], but I need the entire picture. – Blooment Aug 25 '20 at 18:41