Serializing and de-serializing an associative array in bash using jq - bash

Question

I have some bash code that serializes and de-serializes a single dimensional associative array in bash using jq. It does what I want for now, but I have two issues.
The first issue is, this code feels really klunky. Especially the serialization part. Is there a better way to do this? Either with jq or some other way?
The second issue is, I can deserialize nested data (.e.g, with {"data":{...}}) but I can't figure out how to wrap the output in the same nested structure. How can I recreate the original structure?
Edit: Clarification. What I want to be able to do is, with the commented json, json='{"data": {"one": "1", "two": "2", "three": "3"}}' in the example code and have the final result of
json='{"data": {"four": "4", "one": "100", "two": "2"}} dumped.
I can read in the 'data' structure and assign the key/values correctly, but I'm not having any luck in figuring out how to embed the {"four": ...} construct into the "data": {...} object.
Edit 2: The answer to my second issue, in combination with peak's answer is the following:
for key in "${!aaname[#]}"; do
printf '%s\n%s\n' "$key" "${aaname[$key]}"
done | jq -SRn '.data = ([inputs | {(.): input}] | add)'
The code is:
#!/bin/bash
#json='{"data": {"one": "1", "two": "2", "three": "3"}}'
json='{"one": "1", "two": "2", "three": "3"}'
#------------------------------------------------------------------------------
# De-serialize data
declare -A aaname
while IFS='=' read -r key value; do
aaname["$key"]="$value"
done < <(echo "$json" | jq -r '. | to_entries | .[] | .key + "=" + .value ')
#done < <(echo "$json" | jq -r '.data | to_entries | .[] | .key + "=" + .value ')
#------------------------------------------------------------------------------
# Manipulate data
# Change existing value ...
aaname['one']='100'
# Add element ...
aaname['four']='4'
# Remove element ...
unset aaname['three']
#------------------------------------------------------------------------------
# Serialize data
# Why can't I use ${#aaname[#]} in ((...))?
total="${#aaname[#]}"
count=0
{
printf '['
for key in "${!aaname[#]}"; do
printf '{"key": "%s", "value": "%s"}' "$key" "${aaname[$key]}"
((++count < total)) && printf ','
done
printf ']'
#}
#} | jq -S ' . | "data{" + from_entries + "}"'
} | jq -S ' . | from_entries'
# gives
#
#{
# "four": "4",
# "one": "100",
# "two": "2"
#}

Answer 1

It would be less klunky, and perhaps a bit more robust, if instead of:
jq -r '. | to_entries | .[] | .key + "=" + .value ')
you had:
jq -r 'to_entries[] | "\(.key)=\(.value)"'
And similarly you could replace the for loop used to create the JSON object with something like:
for key in "${!aaname[#]}"; do
printf "%s\n" "$key"
printf "%s\n" "${aaname[$key]}"
done | jq -Rn '[inputs | { (.): input}] | add'
Regarding the second issue, I'm afraid your question isn't so clear to me.
What format are you expecting for the non-JSON representation?
How generic a serialization/deserialization solution are you expecting?
In this connection, you might like to look at the output of jq --stream . <<< "$json"
for various JSON texts.