Ttdfjt

There is a widespread perception in non-traditional congregations that the Torah scroll can count as a tenth to make a minyan.

However, the Code of Jewish Law does not mention that. It only says that some authorities allow a six-year-old boy to count as the tenth in a minyan, provided he holds a Chumash or Sefer Torah and understands what he is doing [Shulchan Aruch, Orach Chayyim 55:4]. Some, led by the Ri (Rabbi Isaac ben Samuel the Elder of Dampierre) reject this view. The current practice is that some permit it only in extraordinary circumstances [The Rosh and Mordechai and Hagahot Maimoni Chapter 9 of the Laws of Prayer].

So, is there any basis in our tradition for this practice in non-traditional synagogues?

R David Sperling at yeshiva.co here addresses your question and brings a number of rejected opinions - to be clear the halacha remains that a Torah scroll does not count as a tenth in a minyan

In regards the question of using a Sefer Torah as the "tenth man" in a
minyan – yes this does have a vague hint of a source. Firstly, the
Talmud (Brachot 47b) when discussing forming a minyan for saying zimun
before grace after meals (with Hashem's name in it), says "Said Rav
Huna, "Nine and the Aron [Kodesh] join up [to be counted as ten]". The
Talmud immediately rejects this and says "Is the Aron a person!". This
then may be the (rejected) source for the idea that the Sefer Torah
counts for a minyan.

However, we do find some reference in halacha to some form of using a
sefer Torah for a minyan. The Shulchan Aruch (Orach Haim 55,4) talks
about including a boy less than bar-mitzvah age as the tenth for a
minyan, and writes that this is forbidden. The Rema adds that there
are those that in a time of need do rely on using a child, as long as
he is holding a Chumash in his hands. The overwhelming consensus of
Rabinic opinion is not to rely on this opinion even in times of need
(see Mishna Brurah there).

The source for the idea that a minor holding a chumash or Sefer Torah
might be counted for a minyan is discussed by the Rosh (Berachot 7,
20) where he discusses at length the opinions that allow one child to
be counted towards a minyan, and he writes "The only source for this
[counting a child who is holding a chumash] is Pirkei d'R. Eliezer,
regarding Ibur Shanah [declaring a leap year]. There, it mentions a
Sefer Torah. It says that R. Eliezer requires ten for Ibur Shanah, and
if we lack one, we bring a Sefer Torah. It does not say that the minor
holds it. Even if there is such a source regarding Tefilah, this is
only for a Sefer Torah or Chumash, i.e. one Sefer of the Torah written
on parchment. Chazal did not have [printed] Chumashim like we do.

The Yerushalmi says "a minor and a Sefer Torah, we include them for
10." This means a minor or a Sefer Torah, just like nine men and the Aron. The Halachah does not follow the Yerushalmi. Some texts of the
Yerushalmi say "a minor and a Sefer Torah, we include oto (him, or
it)." This is like the custom (that the minor holds the Sefer). Or,
perhaps it means that a minor may be counted among the seven required
Aliyos."

From here we see that in fact there is a situation where a Sefer Torah
makes up a minyan (for declaring a leap year) according to one
opinion, and perhaps even for a minyan for prayer, according to the
Yerusalemi Talmud. However, the halacha is not like this source, and
we do not use a Sefer Torah (nor a child) as a "tenth man" for a
minyan. In extreme situations a community should consult there Rabbi
as to the advisability of relying on the minor opinions that allow
counting a child who is holding a Sefer Torah for a minyan.