how does one combine conditionals into one "when" statement?

Your second attempt...

- name: Override default path
  set_fact:
    repo_url: "https://someUrl/releases"
  when: '"development_" not in web_version and 
         "feature_" not in web_version'

...seems syntactically correct. In a playbook like this:

- hosts: localhost
  gather_facts: false
  vars:
    repo_url: "https://someUrl/development"
  tasks:
  - name: Override default path
    set_fact:
      repo_url: "https://someUrl/releases"
    when: '"development_" not in web_version and 
           "feature_" not in web_version'

  - debug:
      msg: "URL={{ repo_url }}"

If we run it like this:

ansible-playbook -e web_version=development_ playbook.yaml

We see as output:

TASK [Override default path] ****************************************************************************
skipping: [localhost]

TASK [debug] ********************************************************************************************
ok: [localhost] => {
    "msg": "URL=https://someUrl/development"
}

And if we run it like this:

ansible-playbook -e web_version=1.4.44 playbook.yaml

We see:

TASK [Override default path] ****************************************************************************
ok: [localhost]

TASK [debug] ********************************************************************************************
ok: [localhost] => {
    "msg": "URL=https://someUrl/releases"
}

That seems to do exactly what you want. Note that you're looking for the string development_ (with a trailing underscore) in your when statement, rather than development as in the first example, but that's an easy fix.

---

While your code works just fine, I find it helpful to use one of YAML's quote operators for writing multi-line when statements, since it avoids me getting confused by nested quotes in the expression:

- hosts: localhost
  gather_facts: false
  vars:
    repo_url: "https://someUrl/development"
  tasks:
  - name: Override default path
    set_fact:
      repo_url: "https://someUrl/releases"
    when: >-
      "development_" not in web_version and
      "feature_" not in web_version

  - debug:
      msg: "URL={{ repo_url }}"

---

Re: your update, this doesn't work...

- name: Override default path
  set_fact:
    repo_url: "https://someUrl/releases"
  when: ('"development" not in web_version')

...because of bad quoting. You are effectively writing:

when: ("a string")

And a non-empty string evaluates as true in a boolean expression. Always put the quotes at the beginning of the expression. E.g., this works just fine:

when: >-
  ("development" not in web_version)

As does the syntactically identical:

when: '("development" not in web_version)'