multiline - What is a good alternative for the IEEEtrantools package? - Stack Overflow

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I am a frequent user of the IEEEtrantool package (giving the IEEEeqnarray environment). Initially it started because I often want one single and centered equation number in a multi-line equation. Later I needed the great flexibility of the IEEEeqnarray(box) option. But I have read that it is advised not to use this package any longer (I do not remember where I have read this and what the arguments were). In order to give you an idea what kind of equation I often make I made a code containing three typical equations.

I have two questions:

1. Is it true that IEEEeqnarray is not advised? and what are the reasons?
2. What would be the best (most flexible) alternative?

Here is the code:

\documentclass[a4paper,11pt]{report}
\usepackage[retainorgcmds]{IEEEtrantools}
\usepackage[most]{tcolorbox} 
\usepackage{amssymb}

\begin{document} 
First example:
\footnotesize
\begin{equation}
\begin{IEEEeqnarraybox}[][c]{rccl}
e_a:\,  &\mathcal C^\infty(\mathbb R^m)&\longrightarrow&\mathbb R\\
&f&\longmapsto &e_a(f)\equiv\left(\frac{\partial}{\partial x^a}\right)_p
\end{IEEEeqnarraybox}\quad\text{and}\quad
%
\begin{IEEEeqnarraybox}[][c]{rcl}
\tilde e_a:\, &\mathcal C^\infty(\mathbb R^n)&\longrightarrow\mathbb R\\
&g&\longmapsto \tilde e_a(g)\equiv\left(\frac{\partial}{\partial y^a}\right)_{\phi(p)}
\end{IEEEeqnarraybox}.
\end{equation}
\normalsize

Second example:
\begin{equation}\begin{IEEEeqnarraybox}[][c]{rccccl}
df_p:\, &T_pM&\xrightarrow{\,\sim\,} &T_{f(p)}\mathbb R &\\
        &X   &\longmapsto\,            &df_p(X):\, &\,C^\infty(\mathbb R) &\xrightarrow{\,\sim\,}\mathbb R\\
                &        &                                           &               & g           & \longmapsto df_p(X)(g):=X(g\circ f).
\end{IEEEeqnarraybox}\end{equation}

Third example:
\begin{equation}\begin{IEEEeqnarraybox}[][c]{rl}
\tcbox[nobeforeafter]{$
A_jf_i=\sum_{k=1}^\lambda \Gamma(A_j)_{ki}f_k,\qquad i=1,2,\cdots,\lambda;\;j=1,2,\cdots,n, $}
\end{IEEEeqnarraybox}
\end{equation}
%
\end{document}

Can these equations be reproduced with some other package?

I tried align and split but these cannot replace IEEEeqnarray option fully.

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