How would you design a note taking app?

I'd start by asking clarifying questions about the note-taking app we plan to design.

Q1: What type of company are we & what is our goal with launching this app? [Established / start-up, Catering to certain TG / generic / Extension of any of our existing products / New Market entry etc.]

Q2: What will be the scope of the app? [Physical scope - Handheld/ Device; Device specific - Desktop/Mobile, Region-specific]

Q3: Do we have any competitors in the space, should we think about our differentiation too while designing? [Assuming Notion, OneNote, etc. already have an established product and a good market share]

Then I'd start exploring the user personas who I feel would be the right fit for the app.

UP-1: B2B users - Organization employees; would use for general notes jotting meeting MOMs, making daily to-do's. Could narrow it down to people with a lot of cross-functional collaboration rather than individual contributors (if required) 

UP-2: 
B2C users - People in the age range of 18-22 [Students]; tech-savvy, would want to record their school/college work, would want to keep track of personal expenses, plans, etc. wants to maintain a single repo of all the information. 

B2C users - People in the age range of 22 - 30 [Professionals];  tech-savvy, would want to be productive, would want to keep track of work and personal items to be on top of things.

Based on the responses to clarifying questions, and responses from the interviewer on user persona, I'll go ahead and pick one persona. 

I'd pick Students since it's the TG with more TAM and the competitors aren't exclusively competing for market share there. Also later we'll be able to extend the TG to age 22-30 with existing customers.

I'll start listing down features of the note-taking app for the user persona based on their needs.

F-1: The app should be supported for all devices and preferably allow physical scope too [Handheld and Desktop] 
Hypothesis for F-1: Students would take notes in classroom lectures using handheld, they would later want the information synced across devices for easy access and consumption of information

F-2: The app should support integration with third-party apps like G-Classroom, Payment services, etc. for quicker and easy access to their recorded information. 
Hypothesis for F-2: Students would get their classwork, and homework assigned in G-class or any other third-party LMS, integration to the same would help. Payment services to help easy, quicker access to their financial information.

F-3: The app should allow easy sharing of information across apps.
Hypothesis for F-3: Students would use the app both on a personal and social level where they would want to share information with their friends, batchmates, even parents, etc.

F-4: The app should have an option of offline access [Read, Write], offline downloads, physical downloads [print]
Hypothesis for F-4: Students would use the app in areas of poor and zero network connectivity where this would not serve as a blocker in usage. Offline downloads for saving personal data, physical downloads for probable personal convienance.

F-5: The app must support the writing of information in different formats [Text, Audio, Video, Files, Tables, Pages]
Hypothesis for F-5: Students would consume information in different formats and support of them would help in quick adoption and engagement.

Based on the solutions listed above, we can prioritize based on the Impact-Effort matrix. 

High Impact, High Effort: F-1, F-2
High Impact, Low Effort: F-5
Low Impact, Low Effort: F-3 [Since we could focus on adoption of the individual users first]
Low Impact, High Effort: F-4 [Connectivity is ubiquitous in our TG and market]