[New answer after comments]
There are several ways to consider the placement of an object in a text reflow system. Primarily TeX has the concept of floats. That is an object can nominate zonal areas where text may flow around the object and it seems that is what you are requesting here (The smooth flow of text around an inline floating object) Such an example is shown in the lower part of this example page.
The position of where the float may move to is discussed here
How to influence the position of float environments like figure and table in LaTeX?
The alternative to an inline float is finishing the text in a fixed location which will generally result in a ragged finish to the previous paragraph, see upper example.
There are possibilities to fix the object at a nominal position and flow the text before and after (or optionally wrap text on one or two sides) for single side the wrapfig
package is fairly good. However for two sided say midway in a doublecolumn it can be problematic see the older answer after this mwe.
\documentclass[12pt]{article}
\usepackage{fullpage}
\usepackage{blindtext,letltxmacro,xcolor,xparse,lipsum}% for demo only [start]
\LetLtxMacro{\blindtextblindtext}{\blindtext}
\LetLtxMacro{\blindtextBlindtext}{\Blindtext}
\RenewDocumentCommand{\blindtext}{O{\value{blindtext}}}{%
\begingroup\color{gray}\textit{\blindtextblindtext[#1]}\endgroup
}
\usepackage{showframe}% for demo only [end]
\usepackage[linguistics]{forest}
\renewcommand{\baselinestretch}{1.15} %modified for ilustration
\begin{document}
\blindtext[1] \textbf{Here we see (or don't as the case may be) The following tree-diagram illustrates blah... [fixed ending]}\begin{center}[float is n/a]\newline\begin{forest}[(Fixed here by a centre environment)\\$ \omega $[Physical][Mental]]\end{forest}\end{center}\textbf{The idea is that a distinct structure blah.1...}%
\blindtext[1] \textbf{Here we see (or dont as the case may be) The following tree-diagram illustrates there is not enough room blah... .[floating]}\begin{figure}[bh]\centering\begin{forest}[(Float here as a figure environment)\\$ \omega $[Physical][Mental]]\end{forest}%
% replace this comment but KEEP one blank line
We can add some floating comment
\end{figure}
The idea is that a distinct structure blah.2...\blindtext[1]
\lipsum[3]
\end{document}
[OLD answer with fragile cutwin]
This is very fragile especially combined with the 1.5 baselinestretch you specified (it works better if that is the default of 1. An adjustment is possibly needed to the cutwin
package for recalculating odd baseline values. NOTE that cutwin
prefers the lines to be specified exactly to suite the number of the lines it is inserted within.
"How can I place this box within the text such that Latex can
determine its location within the final document in a way that text
continues smoothly on either side?"
\documentclass[12pt]{article}
\usepackage{fullpage}
\usepackage{cutwin}
\usepackage[most]{tcolorbox}
\usepackage{lipsum}% for demo only
\usepackage[linguistics]{forest}
\renewcommand{\baselinestretch}{1.5}
\begin{document}
\def\windowpagestuff{\centering \begin{minipage}{0.85\textwidth}
\begin{tcolorbox}[fit basedim=50pt]\centering\begin{forest}[$ \omega $[Physical][Mental]]\end{forest}\end{tcolorbox}~%
\end{minipage}}
\begin{cutout}{2}{0.33\textwidth}{0.33\textwidth}{6} % {lines above}{space to left}{space to right}{lines high}
\noindent The following tree-diagram illustrates that both Physical and Mental attributes are a result of $\omega$ ...The idea is that a distinct structure is achieved by trial and errors....\lipsum[66]
\end{cutout}
\lipsum[66]
\end{document}