Retina 0.8.2, 326330 bytes

^((\()|(?<-2>\))|[^()])+
$&$#2$*)
[^ (](?=\()|\)(?=[^) ])
$& 
{%`^(( *)\(+?([^() ]+ |((\()|(?<-5>\))|[^()])+(?(5)^) )+)(\(([^() ]+ |\(\) )*\([^)])
$1¶$2 $6
 ¶
¶
%+`^(( *)\(([^() ]+|((\()|(?<-5>\))|[^()])+(?(5)^))( [^() ]+| \([^()]+\))+)( [^() ]+| \([^()]+\))+$
$1¶$2$7
%+`^(( *)\(([^() ]+|((\()|(?<-5>\))|[^()])+(?(5)^))\)) 
$1¶$2

Try it online!Try it online! Link includes test cases. Explanation:

^((\()|(?<-2>\))|[^()])+
$&$#2$*)

Use a .NET balancing group to count how many extra (s there are and append that many trailing )s.

[^ (](?=\()|\)(?=[^) ])
$& 

Insert spaces before (s and after )s where necessary.

{`

Repeat until no more transforms can be made.

%`^(( *)\(+?([^() ]+ |((\()|(?<-5>\))|[^()])+(?(5)^) )+)(\(([^() ]+ |\(\) )*\([^)])
$1¶$2 $6
 ¶
¶

Split lists of nesting level 3 or more.

%+`^(( *)\(([^() ]+|((\()|(?<-5>\))|[^()])+(?(5)^))( [^() ]+| \([^()]+\))+)( [^() ]+| \([^()]+\))+$
$1¶$2$7

For those lists, where there are only lists of nesting level 0 or 1 left, put all but the first on their own line. (We need to check explicitly to ensure that the list was in fact split in the first place.)

%+`^(( *)\(([^() ]+|((\()|(?<-5>\))|[^()])+(?(5)^))\)) 
$1¶$2

Lists of nesting level 0 or 1 after a list of nesting level 2 or more also need to go on their own line. (We know they can't have also nesting level 2 or more because they would have been split off earlier, so we don't actually need to check their nesting level.)