Overlapping String-Blocks

JavaScript (Node.js), 24 bytes

Saved 2 bytes thanks to @Grimy

Assumes that the returned string is printed on a terminal that supports ANSI escape codes. Contains the unprintable character ESC, which is escaped (no pun intended) as \x1B below.

a=>`\x1B[2J\x1B[H`+a.join`\x1B[H`

This doesn't work on TIO, but you can Try it online! to see the raw output instead.

How?

The CSI sequences used are:

• ED (Erase in Display):

  ESC[2J

  where \$2\$ means "clear entire screen"

• CUP (Cursor Position):

  ESC[H

  which means "moves the cursor to row \$n\$, column \$m\$" where both \$n\$ and \$m\$ are omitted and implicitly set to \$1\$ (top-left corner of the screen).

Example output

R, 120, 111 110 107 bytes

function(x,`!`=ncol,M=array('',Reduce(pmax,Map(dim,x)))){for(m in x)M[1:!t(m),1:!m]=m
write(t(M),1,!M,,'')}

Try it online!

A function accepting a list of matrix of characters (3D input is accepted).

(as you can notice from the byte count, this is not very easy to do in R...)

• -9 bytes thanks to @Giuseppe
• -4 bytes thanks to @RobinRyder

Jelly, 3 bytes

a/Y

Try it online!

Hadn't used Jelly in a while but I thought the challenge in the comments was beatable. Very directly uses logical and (a) to perform the stacking operation between each element of the input (/). Y is used to print in the required format.