Thank you for the clues! I had to run the solution from @DmytroMitin through the debugger to grasp what was happening.

package dynamicProperties

import scala.language.dynamics

class DynamicProps(val props: java.util.Properties, val propName: String = "", val prop: Option[String] = None) extends Dynamic:
  def updateDynamic(name: String)(value: String): AnyRef =
    val newName = if propName.isEmpty then name else propName + "." + name
    props.setProperty(newName, value)
  def selectDynamic(name: String): DynamicProps =
    val newName = if propName.isEmpty then name else propName + "." + name
    val newProp = Option(props.getProperty(newName))
    DynamicProps(props, newName, newProp)
  def applyDynamicNamed(name: String)(args: (String, String)*): Any =
    if name != "add" then throw IllegalArgumentException()
    for (k, v) <- args do
      props.setProperty(k, v)

  override def toString: String = prop.getOrElse("n/a")

This is my test code.

import dynamicProperties.DynamicProps
import org.scalatest.funsuite.AnyFunSuite

class DynamicPropsTest extends AnyFunSuite:
  test("Set username") {
    val sysProps = DynamicProps(System.getProperties)
    sysProps.username = "Fred"
    assert(sysProps.username.toString() == "Fred")
    sysProps.xxx.yyy = "bbb"
    assert(sysProps.xxx.yyy.toString() == "bbb")
  }
  test("Assign java.home") {
    val sysProps = DynamicProps(System.getProperties)
    val home = sysProps.java.home.toString()
    val javaHome: String = System.getProperty("java.home")
    assert(home == javaHome)
  }
  test("Add key/value pairs") {
    val sysProps = DynamicProps(System.getProperties)
    sysProps.add(username="Fred", password="Secret")
    assert(sysProps.username.toString() == "Fred")
    assert(sysProps.password.toString() == "Secret")
  }

For setting the properties with multiple periods, I noticed the code jumped to selectDynamic before going to updateDynamic .