Remove selected character delimited paragraphs using an inverted negative lookahead across multiple lines

Question

I have this input string:

string = '''p1 = {
s,
},

p2 = {
{s,
},

p3 = {
s,
},

p2 = {
}s,
},'''

I am trying to replace all paragraphs starting with p2 = { and ending with }, and end up with this new expected output string:

p1 = {
s,
},

p3 = {
s,
},

I can achieve this without using a regex by just looping over the lines. But how would I do it with a regex?

This method using re.subn does not make any replacement and I don't understand why not:

import re
repl = ''
pattern = r'p2 = {.*?},'
new_string, number_of_subs_made = re.subn(pattern, repl, string, 
re.MULTILINE|re.DOTALL)

This method using re.findall seems to be able to find all matches:

import re
pattern = r'.*?(p2 = {.*?},).*?'
m = re.findall(pattern, string, re.MULTILINE|re.DOTALL)
print('\n'.join(m))

It prints this output:

p2 = {
{s,
},
p2 = {
}s,
},

There is a question on how to emulate grep -v and exclude lines with pattern matches, and the answer suggests using a negative lookahead: Regular expression to match a line that doesn't contain a word?

And there is a question on how to use negative lookahead across multiple lines here: Regex with negative lookahead across multiple lines

Would it perhaps be possible to somehow invert that negative lookahead and print the lines that do not match?