There are apps which report the exact cell tower that you're connected to
at any given moment but which of the identifiers that these apps provide
tells me the exact cell tower and sector antenna unique identifier?

The stress of this question is on the word "unique" since just knowing the
cell tower location in an Internet lookup database is not as useful as
knowing the exact identifier for the exact sector antenna connection.

This is an example of the sets of numbers which these apps report.
https://mobiletechtalk.co.uk/wp-content/uploads/2019/11/2019-11-01-12.42.46.jpg

There is a mobile tower TAC, PCI, ECI & EARFCN reported by these apps.

What is the minimum combination of those identifiers that is exactly the
unique sector antenna the phone is currently connected to?

As shown in this example, every phone can report where it is and exactly
what sector antenna on what tower by what carrier it is connected to.
https://i.ibb.co/kHMpDBn/Screenshot-2021-05-16-14-38-14-934-make-more-r2d2-cellular-z.jpg

MY LOC = 60.384528/56.850208
Serving Cell TAC = 26566
Serving Cell PCI = 31
Serving Cell ECI = 170572549(666299-5)
Serving Cell EARFCN = 3300/21300
Serving Cell FREQ = 2675/2555
Serving Cell BAND = 7(FDD)
My current RSRP = -99 dBm

As compared to this phone which also knows all that same identifying data.
https://mobiletechtalk.co.uk/wp-content/uploads/2019/11/2019-11-01-12.42.46.jpg

MY LOC = -3.247542/55.976644
Serving Cell TAC = 35088
Serving Cell PCI = 349
Serving Cell ECI = 129457524(505693-116)
Serving Cell BANDWIDTH = 5 MHz
Serving Cell EARFCN = 39250
Serving Cell FREQ = 2360 MHz
Serving Cell BAND = 40(TDD)
My current RSRP = -93 dBm

I was hoping others would know this already so looking each of those
indicators up to better understand which are the minimum unique set.
https://www.hawkanalytics.com/a-simple-guide-to-understanding-cell-site-terminology-when-mapping-cellular-call-detail-records/

The TAC is the Type Allocation Code.
Used to create the first 8 digits of the International Mobile Equipment
Identity (IMEI), the number that identifies each unique mobile device on
all gsm networks.

The PCI is the Physical Cell Id.
This is the identifier of a network cell in the physical layer. This
property is limited to 504 values, and therefore needs to be reused in the
network. If the PCI assignment is poorly planned, the risk for network
conflicts is high.

The ECI is the Extended Cell identification or ECGI (Global).
This number consists of the MCC, MNC, eNodeB and Cell ID.

The CGI is the Cell Global Identification for a Base Transceiver Station in
mobile phone networks. This number is used in the GSM and UMTS networks and
is a combination of the MCC, MNC, LAC and the CI.

The MCC is the Mobile Country Code.
The mobile country code consists of three decimal digits and the mobile
network code consists of two or three decimal digits (for example: MNC of
001 is not the same as MNC of 01). The first digit of the mobile country
code identifies the geographic region as follows (the digits 1 and 8 are
not used):

0: Test networks
2: Europe
3: North America and the Caribbean
4: Asia and the Middle East
5: Australia and Oceania
6: Africa
7: South and Central America
9: Worldwide (Satellite, Air?aboard aircraft, Maritime?aboard ships,
Antarctica)

The MCC is used in combination with an MNC (a combination known as an
"MCC/MNC tuple") to uniquely identify a mobile network operator (carrier)
using the GSM (including GSM-R), UMTS, LTE, and 5G public land mobile
networks. Some but not all CDMA, iDEN, and satellite mobile networks are
identified with an MCC/MNC tuple as well.

The MNC is the Mobile Network Code.
The Mobile Network Code is a unique two- or three-digit number used to
identify a home Public Land Mobile Network (PLMN). MNC is allocated by the
national regulator. A MNC is used in combination with the Mobile country
code to derive the Home Network Identity (HNI).

The LAC is the Location Area Code.
The LAC is the unique number given to each location area within the
network. The served area of a cellular radio access network is usually
divided into location areas, consisting of one or several radio cells.

The eNodeB is the Enhanced NodeB which references a group of antennas on a
cell tower. The eNodeB alone does not identify the sector. To identify the
sector or direction the specific antenna faced, you'll need to refer to the
Cell ID.

The GSM Cell ID is the Cell Identity.
It is a generally unique number used to identify each base transceiver
station (BTS) or sector of a BTS within a location area code (LAC) if not
within a GSM network.

The EARFCN is the E-UTRA Absolute Radio Frequency Channel Number.
In LTE, the carrier frequency in the uplink and downlink is designated by
EARFCN, which ranges between 0-65535. EARFCN uniquely identify the LTE band
and carrier frequency.

From that information which every phone easily reports, I should be able to
deduce the exact sector antenna used by any one connection at any given
time.

Specifically, if I have multiple people at the same place, each of us
should be able to instantly determine which unique sector antenna each of
us is connected to.