Have any 20th/21st century Ecclesiologists developed a framework/models for describing/categorising the functions of the visible church?

I have yet to find an academic book or a journal article that provides a research-level model for what a church does. Most I found is on the nature of the church, similar to Avery Dulles's 1987 book Models of the Church, such as Stanko Jambrek's 2019 journal article Church Models for the 21st Century where he reviews a variety of church models in 3 categories (1. formed today, 2. created throughout history, 3. have a foundation in the Word of God). The article also includes an analysis of Dulles's model.

However, below are some pointers for your literature review to come up with a good list/model of what a church does for your coding frame.

Enduring church functions

For a church to thrive and blessed by the Holy Spirit, the church needs to be aware of its proper mandate. Based on the Acts of the Apostles, The Letters of Paul, and the Pastoral Epistles, Rev Mark Feldmeir wrote The Five Functions of the Church for the Clergy Academy of the Mountain Sky Conference of the United Methodist Church:

• Training - Didache
• Worship - Liturgia
• Community - Koinonia
• Service - Diakonia
• Proclamation - Kerygma

How a church implement the NT mandate and organize their activities is of course heavily dependent on its denomination. For a representative example of a Protestant church read the article Church: Six Functions of the Church or for a typical non-denominational Baptist church read the 2019 Southern Baptist Journal of Theology article What are the Essentials of a Local Church? Guidelines for Missionary Ecclesiology which enumerates a local church's functions as follows:

• Worship: public singing, teaching, admonition, celebration of ordinances, giving, testimony, mutual encouragement
• Preaching and Teaching:
• Prayer: adoration, confession of sin, thanksgiving, supplication, intercession
• Baptism and the Lord's Supper:
• Discipleship: individual exhortation, encouragement, mentoring
• Fellowship: build each other up, serving one another, bear one another's burden, etc.
• Accountability and Discipline: intertwined with both discipleship and fellowship
• Generous Giving: to relieve the poor, to advance the gospel around the world, etc.
• Evangelism:
• Missions:

Another way to bring out what a church does is by examining the church officers mentioned in the New Testament:

• Presbyters: Responsible for teaching, preaching, baptisms, pastoral care, leadership, management
• Elders: Responsible for governing and internal affairs
• Deacons: Responsible for external affairs including the caring side of the church, including ministering beyond the community of faith

To the above NT offices many Protestant churches today add / subsume new offices to complete their church organization and hierarchy with:

• Ministries: Sunday school, adult education, music, women's group, men's group, etc.
• Support groups: grief sharing, divorce recovery, substance abuse, etc.
• Missions:
  • local projects: soup kitchen, homeless shelter, etc.
  • regional projects: home repair, habitat for humanity
  • international projects: schools, hospitals, orphanages, missionaries
• Committees: Nominating, Hospitality, Personnel, Finance, Stewardship, etc.
• Board of Trustees: responsible for the property of the church

(source: Don's empirical notes on church officers and church organization, better source to be found)

Church administration and church leadership books

I found that Church administration and church leadership books, especially the handbook / reference style ones, can help populate your coding frame. For example, see the detailed Table of Contents of The Church Leader's Answer Book: A Reference Guide for Effective Ministry which covers (what I think) every foreseeable activity that a church might do to implement the above church functions effectively, although I admit that this book seems to be written more for non-sacramental / non-liturgical / non-denominational churches, and therefore is missing some aspects of what Lutheran / Anglican / Catholic churches are doing.

To give an idea, these are the book's part headings, which in turn are subdivided into about 5-8 chapters each:

1. Administration: Church Management, Church Boards, Meetings, Decision Making, Pastoral Search, Staffing, etc.
2. The Church Office: People, Place, Procedures, Storing Documents, Equipment, etc.
3. Change and Conflict:
4. Construction and Renovating: Deciding, Building Trends, Builders and Architects, Financing, Location, Planning
5. Facilities and Operations:
6. Church Furnishings:
7. Church Finances: Budget, Borrowing, Grants, Giving, Investments, Taxes, etc.
8. Leading Others: Identifying Gifts, Mentoring, Coaching, Making Disciples, etc.
9. The Pastor's Life: Family, Growth, Rest, Finding your place of ministry, etc.
10. Preaching: Audience, Applying the Word, Planning, Style & Delivery, Illustration, Technology, etc.
11. Groups for Growth: Planning programs, Children's Programs, Youth Programs, Prayer Groups, Small Groups, Singles, Special-Interest Groups
12. Pastoral Tools: Counseling, Special Visits
13. Community Outreach: Becoming Outwardly Focused, Assessing Your Community, Meeting Community Needs, Finding Lost People, Assimilating Newcomers, Missions
14. Worship: The Heart of the Worship Leader, Laying the Groundwork, Worship Planning, Worship Leaders and Teams, Technology, Special Services