Implement Minecraft's Rails
Python 3, 394 378 370 328 bytes

def p(s,i,R,C,H='═',V='║'):
 v=i%C and s[i-1]==H
 v|=(i//C and s[i-C]==V)&lt;&lt;3
 v|=(i%C-C+1and s[i+1]==H)&lt;&lt;2
 return' ═║╗══╔╔║╝║╗╚╚╔╔'[v|(i//C-R+1and s[i+C]==V)&lt;&lt;1]
def f(s,i=0):
 t=s.split('\n');R,C,s=len(t),len(t[0]),''.join(t)
 for c in s:print([c,p(s,i,R,C)][c=='.'],end='\n'[:-~i%C==0]);i+=1

Try it online!
A very naive method. Receives as input a string and iterates over its characters. If a character is a point (a placeholder), replace it with the character returned by p.
The function p builds a &quot;4-bits integer&quot; v, where:

if its 1st bit is set, the placeholder has a valid connection with the west;
if its 2nd bit is set, the placeholder has a valid connection with the south;
if its 3rd bit is set, the placeholder has a valid connection with the east; and
if its 4th bit is set, the placeholder has a valid connection with the north.

A invalid connection occurs with a direction when

the rail is on a border of that direction (the first placeholder in the example given by the OP has an invalid connection with the north and the west since it's in the border, so its 4-bit integer is 1010).


the rail of that direction is misaligned with the placeholder (the fifth placeholder in the example given by the OP has an invalid connection with the east since the east rail is misaligned, so its 4-bit integer is 1011).

After this 4-bit integer is built, it returns the corresponding box-drawing character using this integer as index of a string.